For which type of operations? Helicopter emergency medical evacuation service (HEMES), scheduled operators, unscheduled operators with one and two pilot crews, or unscheduled operators with three and four pilot crews?
Have you tried reading the regulation? It's one thing to have a particular question; it's another to not lift a finger to help yourself, and say "explain it all to me." The first is the result of study and effort. The second, pure laziness.
Both duty and rest revolves around the simple concept of a lookback period. At any given point in time, one must look backward from right now, to find rest. That's how duty is determined, and depending on circumstances, a certain amount of rest must be found in that look back period.
Rest, conversely, must always be determined looking forward, or prospectively. That means that rest must be planned in advance, and that an employer or pilot may never look back to a period of time when the pilot wasn't flying, and say "that looks like rest." The pilot must know in advance that rest is coming, and that rest must be free of all duty to the employer. This is a key point, and what defines rest.
Traveling to the airplane locally can be part of a rest period. Travel not local in nature is not rest. Flight time limitations may be exceeded in circumstances that were unpredictable and beyond the control of the operator (and pilot). The same is not true of duty/rest periods. Duty is determined by rest; in other words, if looking back 24 hours, one must have ten hours of rest, then the most duty one could have is 14 hours of duty, by default. The regulation allows exceeding flight time, but not infringing on rest...which means don't go over your duty period.
Duty may end, and yet one may continue to do things for the employer. An example is your have an assignment to fly passengers to Airport B. On arrival, your duty ends. Your employer would like you to reposition the airplane to Airport C, an hour away. You agree to do it. Your employer can't ask you, because that would be duty, but you can agree, and operate under Part 91....often called a "tail-end ferry." This isn't duty time, but it isn't rest time. It is flight time, which counts against your Part 135 totals.
These are the basics.
https://www.ecfr.gov/cgi-bin/text-id...135.f&rgn=div6
Most 135 involves uncheduled operations with one or two pilots, so we can start there. It's covered by 14 CFR 135.267:
https://www.ecfr.gov/cgi-bin/text-id..._1267&rgn=div8
This section limits the pilot to 500 hours in a calendar quarter (Jan-Mar, Apr-Jun, Jul-Sep, Oct-Dec), and to 800 hours in two consecutive quarters (Jan-Jun, Apr-Sep, Jul-Dec, Oct-Mar). It also limits the pilot to 1,400 hours in a calendar year (Jan-Dec).
Daily flight time limitations work using a sliding ruler; they are not a calendar day. Single pilot operations are limited to 8 hours in a 24 hour period, and two-pilot operations are limited to 10 hours flying in a 24 hour period. That 24 hour period is a rolling value; that means that at any given point, one must be able to look back 24 hours and find no more than 8 or 10 hours of flying. If it's 1500 right now, then one must look back to 1500 twenty four hours ago, and find no more than 8 or 10 hours flying. If it's 1600, one must look back to 1600 and find no more than 8 or 10 hours flying, etc. The 24 hour look-back runs continuously. This sometimes confuses people; the flight time limitations aren't by duty period, and they aren't by calendar day, but a continuous, rolling 24-hour look-back.
If you flew 0000z-0800z for 8 hours flying, and then went off duty and into rest, you could start duty again (single pilot unscheduled operations) ten hours later, at 1800z. Looking back 24 hours, you still have 8 hours flying time. While you can go on duty, you're limited by flight time in the 24 hour period. You don't start "dropping" flight time until after 0000z. For example, by 0100z, you can look back and find 7 hours flight time: you're good for one hour of flight time. In fact, if you started flying at 0000z, you'd be okay, as you'd be looking back exactly 24 hours to find only 8 hours of flying (for single pilot unscheduled operations. For two-pilot operations, that would be 10 hours flying time).
Your duty time is the period of time you can be on duty, or available to act for the employer, in a given 24 hour period. This time looks back 24 hours from now. Looking back, you can have no more than 14 hours duty, and must find at least 10 hours rest in the prior 24 hours. That's continuous rest...not two hours here, four there, and four somewhere else. 10 hours continuous rest. Duty is also continuous. If you start duty and stop an hour later, you need 10 hours rest before you can begin duty again. Duty must be preceded by 10 hours rest, regardless of whether it's 1 hour of duty or 14 hours of duty. Failure to ensure this will get you, and your employer violated. Employers will try to get you to do a lot of things. You live and die by the regulations, so far as your pilot certificate goes. Know them. Get in the books and read them and digest them.
Flight time limitations don't just apply to flying you do for your employer. Any outside flying also counts; any commercial flying, that is. If you flying your bumbleweed 2000 personal airplane around the pattern, that's not commercial flying. If you go take pictures of Walmart parking lots for three hours (aerial photography), and spray crops for two, then that's five hours of commercial flying that counts against your 24 hour, and calendar limitations. For this reason, many employers prohibit outside flying unless by express permission, because that limits your services to the employer.
You'll hear "legal to start, legal to finish," most likely. It's chanted and repeated as if it's true, and it's not. It's a myth, mostly. It means that if you're legal to start a trip, and something occurs that extends the trip (weather, etc) that wasn't forecast or planned, you're still legal to finish the trip...but the advice "legal to start, legal to finish" will get you in a lot of trouble, and is only correct in rare and unusual circumstances.
The FAA will accept exceeding flight time limitations (by a small margin) due to unforecast circumstances. The same is not true of rest limitations (gotta find that 10 hours, looking back) and the FAA isn't tolerant of duty violations. If you're on the road and weather or maintenance issues extend the trip, such that you'll violate either duty or rest, you need to park the airplane and get a hotel for ten hours. It's very easy to let an employer justify you into a violation (or worse). Employers will try.
If you do exceed your flight time limitations for the day (8 or 10 hours, depending on if single or two-pilot operation), then you require additional rest after the trip, before you can operate (go on duty and fly) again. Up to 30 minutes over your flight time limitation, you require 11 hours of rest. More than 30 minutes over, but not more than 60, you need 12 hours rest before you can operate again. If you exceed 60 minutes of overage on your flight time limits for the past 24 hours, then you need 16 hours of rest before you can be used by the employer again.
It's important to keep one regulation clearly in mind, that's not found in Part 135. That regulation is 14 CFR 91.13: Careless or Reckless Operation. It is the regulation that the FAA will invoke when taking enforcement action, even if you didn't violate a duty, flight, or rest regulation, but the Administrator (inspector, etc) feels you acted in an unsafe manner. If you are tired, you are tired, and this may simply be the result of being on a day sleep schedule and flying at night. If you're not safe, it doesn't matter if you're within your duty and rest limitations: you're still unsafe. The regulation doesn't address this, except to say that if you operate in a careless or reckless manner, you will be held accountable...and the definition of careless and reckless is wide open for interpretation. You don't get to interpret it. The FAA will do that for you. Accordingly, be safe, conservative, and don't push your limits. This is judgement, and a fine line; you can call "fatigue" at any time and tell the employer you're too fatigued to continue. Do that too many times and the employer will fire you. Its up to you to make sure you show up rested for a flight or duty period. This can never be stressed enough.
This addresses one prong of the duty and rest requirements (unscheduled one or two pilot crews). There are several others, outlined at the start of this post. If those apply, those can be discussed, but you need to read them. If reading the regulation is too taxing ("cause, pilot eyes"), then you may be in the wrong line of work.
Scheduled means no published schedule for your flying. If you're doing the same trip five or more times a week at the same time, the FAA will look at it as a scheduled operation, for which you must hold the correct operations specifications, and you must abide the rules for scheduled flying ("scheduled" is more detailed, but can be discussed if that's what you'll be doing). For unscheduled, think ad-hoc charter. It can be any time. This doesn't prohibit an employer from having a regularly scheduled duty period...not the same as scheduled operations. You can work for an employer and be on duty noon to two AM every day, and have another pilot be on duty midnight to two PM....scheduled duty periods, but still work for an unscheduled operation...because schedule isn't your duty time, it's the times when the flights or trips are conducted. It's actually a lot easier on quality of life if you have a regular duty schedule, even if doing unscheduled charter...but there are a lot of 135 operators that will try to hire the bare minimum number of pilots, and try to keep them on call 24 hours a day.
This comes back to rest...you must have at least 10 hours (or more) of rest and you must know in advance that it's rest. The employer cannot look back to a time when you were sitting idle with no trip, and call that your rest period...unless you knew before-hand that it was rest, and you had no duty to act for the employer during that block of time.
You must also have 13 24-hour periods free of all duty to the employer, within every calendar quarter. Traditionally, that should be 24 hours off within every 7 days, but for unscheduled one or two pilot crews, the regulation isn't spelled out that way, and the employer doesn't have to do it that way.