The keys are
- pitch lots of healthy yeast
- inject lots of O2
- start fermentation cool, then ramp up
Once I started doing all of these things, my beers started tasting better AND much sooner.
Aside from that, choose a lower gravity recipe. Select a yeast that either flocs well, or choose a style where a bit of haze isn't an issue.
I find all beer will taste yeasty when fermentation first finishes... duh, there is a ton of yeast still in suspension. Then for a few days (up to a week, sometimes two), it will taste very grainy/doughy. You can somewhat mask this with a flavourful yeast (ie; weizen), or lots of late/dry hops.