Let's do the easy ones first:
A round hole up to about 1/2 an inch in plastic and then larger ones.
Bet your using the wromg bit?
Practice, Practice and Practice.
1. Procedure is to locate the hole and center punch it. Best to use an automatic center punch.
For precise work, use an optical center punch. I don't have the latter. With an automatic center punch, you can set the amout of force you get with a press. If you don't use the center punch the bit WILL wander.
2. Use Pilot point or bullet bit, e.g. these: http://www.tylertool.com/dewalt-dw1956-16-piece-pilot-point-and-drill-bit-set/dewndw1956,default,pd.html?ref=froogle&origin={adtype}&zmam=31282435&zmas=47&zmac=478&zmap=dewndw1956
The first bit you use should be able to center the next bit.
Drills in thin material make triangular holes.
3. Drill a tiny locating hole. 1/8" or less with a variabe speed drill.
4. Any other large size holes use a Unibit:
https://www.irwin.com/tools/browse/drill-bits/unibit-step-drills once you make a large enough hole to accept the tip of the Unibit.
The Unibit is best used with a drill press. It can grab the material, so be carefull.
5. If you need lubercation, use dish soap and a little bit of water.
Nice recangular holes are going to be a lot tougher. These instructions are for smaller holes and not say a 4" x 4" cut out.
The Unibit, Nibbler and a file. Start with a nicely scribed edge and be carefull not to overextend your mark.
Find the center using lines between the corners. Drill as above, with a round hole.
Now you can drill the corners and use a hand coping saw. The drills in the corner have to be placed exactly right. The coping saw can be threaded through a hole and attached to the saw. Cut some distance away and file or nibble the edges.
Again, practice.
Enlarge the hole with a Nibbler and a file. If at all possible, use a clamped scrap straight edge.