There is a huge array of skills that you can acquire as a DIYer, but your learning curve can be as steep or shallow as you like. If you have some practical skills from your high school education (eg, woodworking) then you just need to find a bit of time to build your confidence in repairing that chair or smartening up that set of shelves. If you have no experience at your disposal then you may be best off enrolling on an evening course; even something relatively laborious like brick-laying may be to your liking.
The main rule, therefore, is "don't be too ambitious". Whether you have dreamt up a great new project or just want something fixed, plan out the entire job from start to finish. If you can't think how you're going to do a particular step, then don't start anything until you've worked it out. There's nothing more depressing for a DIY newbie than a trail of half-finished projects lying about the place.
Be especially careful of projects that involve water or electricity (and especially both!) as these can easily cause lots of damage or injury when they go wrong or if you don't have a good grasp of the science.
Do take care when operating tools of any kind. Even hand tools can hurt you or an innocent bystander quite easily. Always read and follow the manufacturer's instructions, and keep to the maintenance schedule. Accept that everything can wear out; trying to use a tool that is blunt or rattly can produce poor quality work and can even result in serious injury.
Know your limits when it comes to lifting, carrying or manoeuvring; don't be ashamed to ask for help if that sheet of wood is a struggle for you. DIY doesn't mean doing it without anyone else's assistance!