First off - welcome to the line. I know you've worked hard to get where you are and congrats are in order.
Whether I deadhead or jumpseat, I always make my way to the flight deck.
Jumpseating: Have your certificates ready to view upon request. You'll need to treat the flight attendants with dignity and respect when you show up. The lead flight attendant may simply be called "The Lead" or at some airlines they may be called a "Purser". Regardless, you should introduce yourself and tell them that you're here to request the jumpseat. Then ask if they would mind if you slipped up front to say hello? Some flight attendants may take your certificates to the captain and then invite you up after the captain has looked at them, while others may simply let you walk on up to knock on the door. When you arrive at the flight deck door, don't just knock and barge on in. If you find the crew briefing a departure or something, be patient and wait for them to complete their brief. Then you can simply say: "Hi, my name is ___________. I'm with "_________ Airlines." "If you don't mind, I'd like to catch a ride with you to _________." You should reach forward to shake hands then offer your certificates at that time. Be sure to introduce yourself to both pilots. The captain will review your certificates if he or she desires and will most likely engage you in some simple conversation. Where's home? etc. By the way, if you have some sort of snack for the crew - you get big bonus points here.
(FedEx guys love that kind of thing. It keeps their blood sugar up to balance against the caffeine.) Once the captain tells you "Welcome aboard - take any seat in the back....he or she might also ask if there are seats up front in first class." The captain may also ask - "Do you know if we're going to be full?" If you know, answer the question. If you get lucky enough to score a first class seat - enjoy it. A First Class ride is getting harder and harder to get with the cheap upgrades these days. If you get the true jumpseat up in the flight deck, be sure you know where all of your emergency equipment is located and how to use it. The crew should provide a brief to you if you are unfamiliar with the aircraft. Some aircraft have tricky procedures to operate the cockpit windows. Make sure you know how to evacuate "on your own" should you have to do so.
Whether I jumpseat or deadhead, I always make my way to the flight deck in the same manner. As a deadhead passenger, I simply introduce myself in the same manner but I don't ask for a ride. I inform the crew that they have a deadheading crewmember from (airline name) on board in seat XX. Good crews will usually thank you for coming forward and make a small note where you're sitting in case they need your help in an emergency.
When jumpseating and you've received a green light to "ride" the easy part is done. If you have a seat assignment, wait for a space in the boarding line and then you work your way to your seat. If you do not have a seat assignment, then you should probably ask for permission to stow your bags. Ask the lead flight attendant what you should do? Some airlines don't want you to stow your bags ahead of the revenue passengers - others won't care. If you don't have a seat, you're going to have to wait for a vacant seat or occupy a flight deck seat if the aircraft fills up. Please keep in mind that passengers don't know if you work for the airline or not. While your jumpseating, look and act the part. Smile and be polite to the paying passengers as they board the aircraft. They don't know you work for someone else. They don't need to know. The lead flight attendant may also ask you to exit the aircraft and wait in the jetbridge while the rest of the passengers board. This is totally acceptable. You'll be doing a lot of "smiling and nodding" at this point.
Follow the lead's advice and if you need some advice - request it.
As you work your way back to your seat, if you're in your plain clothes, you should introduce yourself to the flight attendants that you pass on your way back. Inform them you're a jumpseater or deadheading crewmember and give them your seat number. It is important to do this whether you're in uniform or plain clothes. Why? It increases CRM. Now both the flight and cabin crews know you're on board and available to help should it be necessary.
I know this is long winded but if you follow these tips, you'll enjoy many years of good deadheading and jumpseating.