It’s easy if you have a 2010 or 2011 unibody Mac Mini, which are the newest models and are thinner than the early 2010 and 2009’s. The bottom unscrews and you can pop the RAM chips in and out, as shown in the Apple Knowledge Base article link below. You still need to be careful of static electricity, but the process is pretty easy.
The early 2010 Mac mini’s are the next easiest – they are thicker (about two inches) than the unibody mini’s – though you need to disconnect one tiny multi connector in order to flip the optical drive and the fan out of the way of the main board.
If you have a 2009 or earlier Mac Mini (also about two inches thick), they’re a bit more difficult and I’d recommend getting an Apple authorized dealer to do it for you, as you need to disconnect tiny cables.
With all non-2010 unibody thin Mac minis, you have to pry the body of the Mac out of the case with a putty knife. There are numerous videos available, such as from OtherWorldComputing.com, such as Mac Mini (2009) Memory Installation Video, so I’d check that out and be sure you’re up for it. You will need some tools and an anti-static bracelet to keep from zapping the components with static electricity.
See this Apple Knowledge Base article Mac mini: How to remove or install memory for instructions on the 2010 Unibody and suggestions for the 2009 models.