R4nier and DayWalker have some good advice.  Do your research, ask a lot of questions and take on the work you feel comfortable with.  There are dangerous areas of vehicles to work on but realize that mechanics do this stuff hundreds of times a day safely.  I had to learn how to do my own work because I could never afford to pay someone to do it.  You'll get a lot of satisfaction by doing it yourself and maybe, be able to help someone else too.

Avoid any suspension spring work until your comfortable with how that operates and how to work on it. On a Corolla there isn’t any fluid with pressure that high until you get to direct injection with a high pressure pump or diesels. At the end of the day you just have to be safe and if your unsure what’s going to happen if you take something apart or how it works then don’t touch it or do your research first 

Also, start simple like with air filter, oil change, transmission fluid change, coolant/radiator change, rotate tires, etc. watch Scotty’s videos and slowly progress as you learn more and become comfortable.  You also don’t have to do everything yourself - that’s OK.  You didn’t say which year Corolla you have, but hopefully it won’t need any major repairs anyways just the regular maintenance.

You can use spring locking tools. And do not mess around engine when it is hot.