cny-bikeman

I would have to agree with the bike shop recommendation at least this time.

If you don't even know what to call a socket wrench you need to take the bike to a shop so they can do a proper adjustment and check the chain for damage. And it's not necessarily cheaper to do it yourself if you do it wrong. In my opinion it would be best to have them give the bike a "tune-up" - basic lubrication and adjustment of gears, brakes, etc. That way your mom will have a safe, properly operating bike and you will have a good base from which to start and some time to learn

If you insist on skipping the shop then start learning by reading about bicycle parts and repair and watching videos online and limit posting individual problems until you understand more of the procedures and terminology. It can be difficult to learn 2nd hand, though, so check to see if a shop, bike co-op or knowledgeable friend can show you the basics. If you do post here, first read check the resources at the head of this forum (READ THIS, Sheldon links).

Remember - no matter what you study something will be left out that you will face eventually. Bike repair, like anything that involves a system of interrelated parts, is not memorizing what to do, but understanding how things relate to and affect each other, so that when you meet new situations you can analyze and solve them. Because a bicycle involves parts performing different functions connected both to a central core and to each other, at angles that affect their interaction, are exposed to the elements and impact, and also interact with the human body, bicycle maintenance can be both one of the most challenging and rewarding activities you can do.

P.S. DO NOT attempt to remove the crank with anything but a crank extractor and make sure you use it properly or you will have an expensive problem.