What do you think of the fair? It seems like it'd be really good for starting something up, but I can't seem to make it go into grabs or usmashes reliably, even L-canceled...
As with all aerials you need to consider: how likely it is to hit (how safe it is), in what position and state the aerial will leave you and the opponent (if it hits and if it doesn't), and what your other options are. So here is what fair does. Fair comes out pretty fast, has pretty crappy rage (pika's body slightly extended horizontally), has decent priority (but will often trade with other aerials), does minor damage, has minimal knockback, has short hitstun (but has multiple hits so can keep them in hitstun for the duration of the aerial), and has little lag afterwards. For this, it can be decent at starting combos or continuing them, but I use it mainly for a little damage and some positioning. When you fair someone, you need to be concerned primarily where you'll be at the end of the aerial (and have the option to fastfall it if you want to change this slightly). So, I'll briefly go over most of the cases where I fair.
Air->ground falling fair -> combo. This is risky and should probably be used the least. It's nice to set up the occasional grab or usmash, but it's very prone to being bated or crouchcancelled. If someone sees you fastfalling an aerial and has time to react, they'll dash/wd back or shield to avoid (which is easy because of fair's meh range) and then punish you. Even though fair has pretty small landing lag, it is still punishable by almost all chars.
Air -> ground falling fair for shield pressure. I do like this a lot for shield pressure however. This is mainly vs. characters with crappy shields, but if you fair through someone's shield (make SURE you land behind them to avoid behind grabbed) and then either tilt/dsmash their shield (or pivot grab if you think you have time), they'll be forced to hold their shield for the whole duration and after a couple of these they no longer have a shield to use.
Air -> air low height -> grab/usmash. I like catching someone with a fair right before they land or right after they jump. The almost non-existant knockback will hold them in the air for the aerial, and after they'll drop to the ground and suffer a little landing lag. This is where you can more easily gets grab or usmashes afterwards, as they can't crouchcancel in the air, have generally less mobility to avoid it, and must spend a short time trying to land (which you intercept with your grab/usmash) before they can. Note that this isn't useful against chars with quick decent nairs (luigi, samus, link, ylink, etc.) as they can just nair after your fair and prevent you from following up.
Air -> air low height -> uair. If you short hop a fair through someone, you can uair right before you hit the ground (no jump in between) and it will pop them up. Then, you can combo them as you see fit. On fastfallers it can set up for a dashgrab/usmash. On medium weights you can chase them into the air with a rising uair or nair/bair. On floaties you can try rising uair->thunder.
Air -> air combo continuer. This also is just approaching someone in the air with fair. You fair through them, and end up behind them or below them. This is most useful to set up another aerial (most commonly uairspike or nair) as it holds them relatively in place while you're travelling through them to somewhere you have more/better options against them (from in front of them to behind/below them).
That's my most common ones. Play around and find where it's useful for you. What you should know about when NOT to use fair is what I've said earlier about the limitations of fair. It has kinda crappy range, has ok priority but will often trade with other aerials (so you hit them once for like 2 damage and they hit you for 12 or whatever their aerial does), and it can be easily cc'd or avoided if they're on the ground. Nair is safer in a lot of cases, but you have to weigh the damage & knockback of nair to the positioning of fair.
When attacking right from the ledge, is it better to uair safely to knock the opponent toward the middle of the stage, or is it worth risking a fair->bthrow to get them offstage?
Alot of what Zig said is true. Whenever you're returning from the ledge to the stage with an aerial, make sure sure sure sure it's going to hit or at least be very difficult to punish. Once you're on that edge people will expect you to return with an aerial, and none of pika's aerials have great range in front of him so they're fairly easy to avoid. What's probably safest if you do want to return with an aerial is uair, but start the uair early so the full duration of the aerial happens before you hit the ground. This makes sure if you hit it will likely hit with the end of uair which pops them behind you off the edge, as Zig mentioned, where you can now try to edgeguard them.
Mix up your returns though. Do this once or twice in a match, but always keep them guessing how you're going to recover. Normal getup, jump getup, waveland on the edge, aerial on the edge, quick attack through the opponent to the stage, etc. This makes it more difficult to punish you returning.