Jumping and Mouthing
Jumping and mouthing are two separate behaviors -- there are dogs who jump at you in greeting without mouthing, and there are dogs (especially puppies) who are very mouthy in play without jumping -- but they often occur simultaneously, they both derive from uncontrolled excitement, and they're both addressed in similar fashion, so I'll cover them together here.
Dogs usually jump and mouth because they're excited to see you (which is why this behavior so often occurs when you get home from work) and want to reach/lick your face. It's an exuberant greeting behavior, and in a way it's a good problem to have, because it indicates that your foster dog is delighted to see you, so your bonding efforts have met with some success. But it's still pretty annoying and it's not likely to endear your foster dog to prospective adopters, especially if he's a big dog, so you should take steps to correct it without damaging your relationship with the dog. Don't punish him for being happy to see you.
The solution to jumping and mouthing behavior is to withdraw your attention completely the instant your dog starts to rear up. Stand up, cross your arms, and turn your back on the dog. If he comes around your side and tries to jump on you again, turn again. You might have to spin in slow-motion circles, but keep your back turned on the dog, don't make eye contact, and keep your arms folded (this prevents your hands from being a target -- many dogs will nip at your hands in an effort to get your attention, and that in and of itself can be enough fun to keep them going). Ignore him utterly.
When your dog finally settles down, click him the instant all four paws hit the ground and reward him with treats (medium- or low-value, nothing valuable enough to get him too excited again), gentle, soothing words, and praise. If he offers a Sit, that's awesome! If he has all four feet on the floor, that's good enough -- you can shape him to an even more polite Sit later. Gradually wait longer and longer after he gets all four paws on the ground before you click and reward, or click and reward repeatedly to encourage him to sustain the behavior, whichever seems more appropriate for your dog (some do better with constant reinforcement, others get overstimulated by that and do better with a quiet wait). Whichever method you use, the goal is to teach him to offer longer durations of quiet, calm behavior. In the beginning, however, his attention span and patience might not be that good, so work toward getting there bit by bit.
It is likely that when you finally deign to pay attention to your foster dog, the renewed attention will be so thrilling that he'll start jumping and mouthing again, which means you have to deliver another dose of the silent treatment. But each episode should be shorter than the last, and eventually (which may be a long eventually, if your foster pup is an excitable high-energy dog or has a long history of being reinforced for this behavior in the past) the polite Sit will become his default greeting.
If your dog is mouthy but not necessarily jumpy -- a common problem with puppies who like to play in this manner and have sharp little baby teeth -- then troubleshooting involves a slight variation on the same theme. Whenever the puppy's teeth come in contact with your skin, even if there's very little pressure, say "Ouch!" loudly and act like you were actually hurt. Stop playing immediately and ignore the dog, standing up with arms folded if necessary to get your point across. Wait for the puppy to offer some calm, conciliatory behavior, then praise and reward him for that.
It may not be quick and it may well try your patience, but responding as outlined above should discourage and eventually extinguish jumping and mouthing behaviors.