2000 Buick Century

From your information, it's hard to say if what you are experiencing is really tranny related or if it's your engine. (Stall, hesitation, etc)

First check your tranny fluid and make sure its at the proper level. (Not low or high, and redish brown with no burnt smell)

If it's out of range or smells burnt, take it in to a shop, as there's not much you can do yourself unless you're experienced with pulling/overhauling trannys.

Also, is your check engine light on? Even if it isn't, you should have your computer scanned, as a competent tech can check the history of your PCM and possibly uncover the cause.

Finally, it may very well be an engine issue. CKP/CMP sensors will cause a symptom similar to the feeling of a tranny slipping, but often you'll have a hard start and/or cut outs. A sever vacuum leak, bad throttle position sensor, etc. Will give you hesitation/stalling problems.