I assumed Vman would come back with more info. He or Axe are muchmuchmuchmuch more versed in the team makeup than I obviously, but i'll give my assumptions on how it'd go.
Pikachu plays pretty well as a less-painful-Fox in teams. He can get in and out of engagements quickly, produce kills (via upsmash or uair gimps), and get to his teammate very quickly (either to help get him out of pressure, or create a 2v1 situation). Yoshi is a little less mobile, but pretty good at just holding place. Getting around Yoshi when he doesn't want you to pass sounds like a tall order in teams. He also does pretty decent damage and has pretty good edge coverage options. I imagine the main thing you want to focus on as Yoshi is to try to control the stage and your opponents while Pikachu isolates and attacks. If your partner is winning a 1v1, don't let their partner get by you to help out. If your partner is in trouble, force yourself into the opponent if possible and give Pikachu a chance to get out to a better position. Otherwise, try to survive and rack up damage. Get kills where you can, do yoshi stuff, etc. Just use your weight and super armor to force yourself into situations where Pikachu needs help, because he is a frail little pokemon.
This is also assuming your partner is capable of playing his role well. He should be using his mobility to his advantage, both to chase opponents and to come to you (either to help save you or doubleteam an opponent). Once you soften them up a bit, Pikachu's usmash becomes scary, and opponents are less likely to be able to crouchcancel his approaches and otherwise stop Pikachu's aggressive game. He should recognize this and figure out which opponent he should focus his aggression on depending on character, percentage, stage position, and how it would interact with what you are doing.
This is mostly supposition on my part though. I have been playing teams for forever, but admittantly have never seriously teamed with a Yoshi before. Vman/Axe let me know if any of that was wrong, and add anything you wish! I know you both lurk here occasionally.