1) Use a textured backing to cut cloth on. If I try to trace and cut my fabric right on my regular sewing board, the cloth slips all over the place. By using felt (glued to a stiff backing), fine sandpaper, or craft foam, I can work with the fabric more easily.
2) When making a lot of similar units, pin and sew them in a large batch. I usually pin them all at once, and then "chain sew" them by simply feeding them one after another into the machine without cutting thread in between units. But I always remember to leave a few centimeters of thread between units! At the end I have a long "chain" of pieced units that I can clip apart and then press all at once.
3) Don't stitch along the bias if you can help it -- patchwork pieces won't fit together at all if they've been stretched. In the photo below there are two triangles that I want to stitch together along the top right edge (the one with the "sew this way" arrow along it). That edge on the bottom triangle is cut along the bias, so I'll make sure to sew with that side facing down. This way the presser foot -- which stretches fabric easily -- will sit on the grain edge, so that the unit's less likely to warp.
Also, when doing triangles I try to sew from acute point to right angle (the arrow!), since the fabric tends to stretch less that way.
4) Store all your pieces in something sealed. Something, anything, a ziploc bag, even, as long as they're all together.
5) Use quilter's cotton. Quilter's cotton is, basically, 100% cotton -- cotton taken straight, if you will. It has a sturdy weave and won't stretch, it's lightweight, and it's easy to press, all of which are good things. This tip should probably have gone first, but as I almost never use it that wouldn't have felt right. At least I can show you what can happen when less stable fabrics are used!
To the far left: the ice cream cone was made of a slippery, stretchy polyester appliqued under a looseweave gingham. Yeah, it warped a lot.
Even the sheer grey fabric and stretchy knit of the patchwork square on the near-left aren't easy to work with, to say the least.
And to the far right I have a close-up of my purple bag. It wasn't quite done in quilter's cotton, but at least both fabrics have a plain weave and aren't too stretchy! See how the corners and edges are a lot neater on this one?