I was surprised how easily my last headset went in. A bit of grease on the headset then pressed in using my homemade press (about a fiver for the length of threaded bar a few nuts and washers, topped of with a couple of wooden offcuts) and a final wee tap with a rubber mallet just to be sure. Just make sure it goes in straight.
Cyclus and X-Tools do some very affordable headset presses (although you do need to be careful that you get the right size). I’ve progressed from taking bikes into the LBS to fix punctures (years ago) to building up my own bikes and it’s really rewarding.
Pressing headsets isn’t hard but for my piece of mind I’d rather use the proper tool.
For removal, Get an old bit of largeish copper pipe (22mm works OK, larger the better), cut a slit down it lengthways for about 8 inches, then tease it apart. pop in headtube, apply hammer. Tada, budget removal tool.