I receive money from royalties and much of it is still a mystery to me. The most thorough "standard explanation" you can get of this is from a text on the business and legal aspects of music (something like This Business of Music). However, it's doubtful just how closely the system works to the theoretical stuff you'll see in those texts. A lot of questionable and shady things still seem to occur with royalties. A lot of what's a mess about it seems unintentional to me--simply wonky reporting systems, a lot of disorganization, etc. Some of what's questionable--and of course shady--about it is intentional.
There are royalties from album sales and there are publishing (songwriting) royalties. If you're an artist who is under contract with a record company--so a solo artist, a member of a band, etc., your contract is going to specify some royalty rate you receive from sales of your album. When you're just starting out, the rate is going to be low, and after the record company deducts all of their expenses and recoups their advance, you might not have much money to show for it, if anything. There have been instances of bands whose first album or two did okay sales-wise who ended up still owing the record company money after that.
If I recall correctly, Angel is an example of a band that finished the game in the hole to their record company (Casablanca), even though they had 7 albums and were moderately successful financially at one point.
It's a complex issue, as in the past, there have been many cases of record companies intentionally screwing over artists financially, and artists ALWAYS think that's happening when they know they had some sales yet they are barely (or not at all) seeing any money, but there really are a lot of expenses that record companies incur getting an album on the market and (hopefully) trying to promote it, and they also need to pay their employees and try to make some profit.
Anyway, you'll make more money if you were credited as a songwriter, too, as you'll also be due publishing royalties from the album. And that fact has caused some dissent in some bands--even to an extent where it's broken some bands up, since some guys are making more money from album sales than others, and it can obviously be debatable just who contributed to writing songs--songwriters in rock bands do not typically come up with everyone's part, especially not drum parts. Coming up with a drum part is writing a drum part, which is part of the song, obviously, and sometimes a very crucial part of a song. It's important to square those issues away early in a band's life. It's usually one of the things I go over before I join a band, or before we even play a note if I'm the one doing the hiring. I prefer a democratic approach, where the whole band is credited with writing all the songs. If it's a band, I see it as a team in the most "noble" sense of that term--all for one and one for all--so that everyone would be contributing, working for the good of the band above all else, and there's no good reason to have some people in the band making more money than others. That can only cause problems--just like if you're working in an office and you find out that other folks doing the same kind of job are making a lot more than you are.
For both of these things, if you've instead done work in a "work-for-hire" capacity--for example, you were a session musician on someone's album, then you're not going to see any royalties (in the vast majority of cases, anyway). You'll instead have been hired for a flat fee or an hourly rate. I've done a lot of work-for-hire gigs in my career. You're not typically going to make a ton of money from those gigs, although you can definitely be comfortable as long as you can keep working and you're getting decent gigs (or working for crazy producers who keep you hanging around even though you're going to be due triple scale, etc.) . . . I've never had any royalty arrangements in a work-for-hire capacity, but I have heard of some people having them.
The part that's the bigger mystery to me, although I vaguely recall having more knowledge of it in the past, is how the radio play, etc. systems work. I know that the general gist of it is that radio stations, and ostensibly public jukebox owners, club owners, etc. are supposed to make periodic payments to BMI and ASCAP. Then BMI and ASCAP figure out who is supposed to get what publishing royalties and pays you--your check from those royalties comes from BMI or ASCAP (depending on your publishing setup). I don't recall how they figure out who is actually getting "air time". I think that at this point, radio stations are supposed to report their actual playlists to BMI and ASCAP, but there's a lot that can go wrong, either accidentally or intentionally, in that system. If I recall correctly, for public jukeboxes, they were randomly surveyed and formulas were based on that, but I don't know how much they even bother with that any longer. Theoretically, club owners are supposed to also make payments to BMI and ASCAP for both songs that DJs play and cover songs that bands play (which is one reason why some clubs only wanted bands doing original music), but especially in the latter case, I don't think anyone has really bothered with it in a long time. Those aspects of the business seem to be the biggest mess, in my opinion.
You can also make money, not just as a songwriter, although again you'll usually make extra as a songwriter, by licensing your music for various uses--films, advertising (TV commercials for example), video games, etc If it's the original recording that you're licensing, you're also producing more money for a record company in most cases, as they typically own the copyright on the sound recording (which is different than owning the copyright on the song itself). That they own copyrights on the sound recordings, by the way, is why you often see odd compilations hit the market all of a sudden--often long after the material was recorded. The record company is trying to milk some more money out of the sound recordings that they own. These can often be released without the artists even being aware of it.
As for copyright expiration, the current law is that works remained copyrighted for 70 years after the death of the longest surviving author. There are ways to renew copyrights beyond that, however, but I do not understand that so well (and neither do I need to worry about it--usually it's folks who are the heirs to your estate who would worry about it).
Can you be comfortable indefinitely from just one big hit? In my experience and understanding, almost definitely not. For one, if you've only had one big hit, you wouldn't have been under contract to any record company for very long, so your royalty rate would have been low, and a lot of what you made probably went to pay the record company back. Heck, even Lady Gaga claimed not too long ago that she hasn't made that much money from music yet. I believe her, for the reasons I mentioned above. Also, even though she's sold plenty of concert tickets, she's had big productions that cost a lot of money to do. She'll probably only become rich from music if she remains close to the level that she's attained for at least a few more years. You could possibly see periodic income from one big hit, especially if it's being licensed for other uses, but it probably wouldn't be enough to live comfortably on for any length of time.
Unfortunately, I've not been a part of any big hits, but I know and have known enough people who have been. Just for one example, one person I've worked with before was in a band who had a number of big hits in the late 60s, the band has been very well regarded since then for the most part, so they still regularly sell albums, their music is still regularly licensed, he's had a decent solo career, he kept performing live (and still does) since then, etc., and when I worked with him the first time (in the mid 90s) he was only making about 30-35k per year--that was his total income, from his then-current activities plus what he was getting from royalties, licensing, etc. Some of the problem there might be bad contracts, and it's my understanding that that was a more common problem in the 60s and prior, but still, it was difficult to believe that that was this person's income (of course, maybe it really wasn't, but I didn't have a very good reason to disbelieve him). I've worked with him again a few times since then, but he hasn't talked about his income again, and it's not something I'd ask about.
I'm certainly no expert on this stuff, though--my understanding comes from trying to understand why I am getting paid what I am (or why I'm not getting paid at all) for music that I've performed and written.