Just took (and passed!) the operative section of the WREB doing two slot preps on DO lesions. My advice would be to try not to rely on wedges or placing a matrix... as your experience tells you, it still won't prevent you from nicking the adjacent tooth if you don't have good control over the handpiece. Find a good solid fulcrum and don't start cutting until you know you have a stable position. Use a bur you feel comfortable with... I like using a carbide 256 (or even a 330), but you can use a tapered diamond too. A Carbide bur seems to give more control than diamond since it's less efficient at cutting. It's also nicer to the adjacent tooth if you do slip. If you are still in preclinic cutting plastic teeth, enamel gives much more resistance than the plastic typodont teeth. It's much easier to control on real teeth.
Rather than going straight into the embrasure, try to leave yourself a little shell of enamel and start prepping your box without touching that very outer surface that's in contact with the adjacent. Focus on your angulation and make sure you aren't tilting the bur mesial-distal and that you are parallel with the long axis of the tooth. If you get it right, by the time you get down to the gingival aspect of the contact, you should be in the right spot and the enamel will usually just flake off. If not, try using hand instruments like a GMT, hatchet, or chisel to chip it away, or slowly work your bur towards the contact while moving buccal-lingual to remove the remaining enamel. I don't know if your school has it, but I really like using an oscillator to open the contact once I'm close (one side of the tip is diamond coated and the other is not, so you can rest it against the adjacent tooth while bevelling the margin and removing the lip of enamel formed by the round burs.) Practice, practice, practice. If you nick the adjacent tooth, polish it out with a polishing strip or soflex disc, but it's obviously best to avoid this when possible.
Hope this helps.