I'm going to agree and disagree with Deserter! Sound like a politician, but it does depend on what sort of acrylic it is - generic name for a whole host of non wood blanks. Is it acrylester, polyester, acrylic, crushed velvet (one of the former crushed and mashed and reformed) and then theres the genesis range from woodturningz which are different to all else.
Warning one which has been mentioned - heat and drilling, drill fast but back out the drill often. If using a drill press make sure that you have a block of dense wood under the acrylic, drilling through to pine or the like can still mean that the drill exits at speed and shatters the blank.
Second trick, study the pen you are turning, look at the dim of the finished acrylic, look at the translucency of the blank and paint the tube and the inside of the drilled blank, the latter with one of those thingys that you do the ear gardening with.
Use a toothbrush to clear the strands of acrylic away as they spiral and clog up everything including your vision. Preferably dont use the toothbrush for its intended purpose again.
I sand with wet and dry and use burnishing cream as the wet, works wonders and then use a dab of ren or microcrystalline.
Hate the stuff, I'm a woodturner not a chemicals processor but the ladies like some of the acrylics at the craft fairs. Have to cleanse the workshop with some olivewood, tambooti, and Juniper turning after the plastic process!