It's an interesting question that can be addressed in a couple of different ways, depending on your league setup.
First, with positional players, the "standard" league is generally going to have a number of games-allowed per position (generally 162). This means that as long as the guy you have in that position is an "everyday player", by the end of the season he'll have used all your games up exactly. It's pretty rare that a player is in the lineup everyday like that without some routine days off or a stint on the DL. So, most leagues will have a tracker somewhere on your roster page that will tell you how many games you are ahead or behind where you should be to reach that target. As long as you don't get too far behind or ahead (say, five games either way), you're doing just fine.
The only spot where this really becomes an issue is your catcher spot, where they get off many more days than other players, and will generally finish a season with only 120-130 games played. This can give you a significant advantage if you pay attention to this and have two viable catchers to swap in and out on their scheduled days off. It takes quite a bit more work to make sure you get all those days you can, but it could mean a difference of quite a few runs, RBIs, and HRs by the end of the season. Unfortunately, it could also cost you a fair few points of average as well if neither of your catchers has a .280+ BA.
Pitching is where this gets a bit more tricky. Some leagues use an inning cap, others us a "games started". The definition of "games started" isn't even really a known quantity either. Does a closer's appearance cost you one of those "starts"? Or is it literally only when a pitcher starts a game. You should pay attention the first week or so to how your moves impact that number to see what the optimal strategy is.
If your league is truly only counting games "started" by your SP, then there's really no reason not to get as many non-start innings as you can out of relievers, even if they're not closers. There are lots of middle-relievers out there you could plug into as many spots as possible (whenever they're not being used by a scheduled SP) and rack up a ton of extra W, SV, and Ks, all while generally helping your ERA/WHIP (if you pick the right relievers).
This information alone, just knowing your league settings and how to exploit them, is generally enough to win you a casual roto-league, almost regardless of how poor of a team you drafted. As long as you have a competent offense, somewhere near the middle-third of the league, you can generally move up a handful of spots just by paying attention during the season. More competitive leagues may be a little tougher, but it's still a fundamental practice that you should pay attention to.