I can give you my perspective, but like Jetjok stated our flying is quite varied. I'm a senior domestic-only narrowbody FO. My trip starts with a commercial deadhead to the outstation that I'll work out of that week. Usually this happens on a Sunday, but can happen Monday morning, depending on how far you live from the outstation. We are required to be in position for a final check in at least 8 hours prior to our first duty period 'show time' in the domestic system. The hub I do all my turns through is Indy so we would leave the outstation in the evening on Monday through Thursday, transit the hub where we sit for 3-5 hours while they unload/reload the freight, then fly back to the outstation for a layover. On Friday morning when we arrive back at the outstation we're scheduled for another commercial deadhead after a legal rest period. Some guys like to go home immediately, but I like to hit the hotel for a few hours of sleep first, then head home. If you're lucky enough to live near the outstation it's even better since you can just drive to the ramp on Monday night, then drive home on Friday morning; or even get home everyday if you're close enough. The company only cares that you show up when you're supposed to move the airplane. They really don't seem to care how you get there or back. In a given month you'd do this for two weeks and have the other two weeks off. Sometimes it's week on, week off, other times the two weeks can follow one another.
Airline tickets (or bus or train) are purchased and the company will pay an amount up to what it would have cost them to move you from Memphis to the outstation and back. This is called your 'deviation bank'. Double deadheaders live and die by the bank and it affects how, where and when you bid certain cities or trips.
There are lots of other ways to work trips here, but this is how my experience has been. I typically do the same thing month after month, but the nice thing by sitting in one seat for years and getting senior is that you can cherry pick something good whenever you want.
One man's meat is another man's poison.
As far as the international dudes doing 'single departure trips' like you asked about, one of them will have to chime in. I'd assume that kind of trip would be pretty senior, but I'm really not sure.
(PS: I only see Memphis twice a year for my PT and PC
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