I see these requests all the time from our Amazon customers, and it has to be the simplest thing to do. If you have seen my EDC video or my post about tools, then all you need is the ten inch vice grips and some silicon tape!
Pipe wrenches and channel locks will also work, in some cases there are two flat sides on the female fitting that allow for a adjustable wrench or spanner to be used. THE MOST IMPORTANT THING IS TO NOT OVER TIGHTEN. Again don’t over do it, which can be easy with any of these tools. I repeat, do not over tighten. I see this all the time here, where a tenant has over torqued the fitting in an attempt to stop a leak and cracked the female fitting. Many of these are plastic and just can’t hold up, and brass fittings are fairly soft and can be stripped.
That is why you use the silicon tape. You could probably use plumbers putty and pipe dope or other sealants, but the tape never goes bad and they usually have them in the impulse bins at the cashwrap of hareware stores. Sometimes its even included in the new shower head. Try to keep it wide as possible and go clockwise around the female fitting like two turns. Cover as much thread as possibly but stay clear of the openings. Screw the new head on with your hand as tight as you can. If you use enough tape this would actually be sufficient, but a 10 degree turn with your wrench will make it snug, using a towel in between to protect the finish if its chromed. One more time, not more than an eighth turn and check for leak. If there is water from the joint, take it off and try again. Many fittings have a gasket inside, if your head leaks start there, but enough sealant around the threads and it won’t matter.
Just a note on removing the old shower head. If the pipe going into the wall starts to turn when turning the head, stop, either employ a second wrench to hold it or consult a professional. Just not us because I have a no plumbing rule.