You need spoons and rim protectors. I cut up a windshield washer fluid bottle, into small strips. Slip them between the spoons and rims. Make one for each spoon and make sure you have then all when you are done...... easy to leave in the rim.
Set up on a good work surface. I use a plastic garbage can and it works great. See photos. The towel is to catch the valve core (which is the FIRST step), when you drop it. Old tires can be a real pain to remove. I pop off one side first, pull out the tube (if you have one). I often go to the second sidewalk (old, stiff tire) and cut around the soft sidewall with a razor knife. Tire then falls off. The remaining “rubber band”, I cut through with a bolt cutter. Falls off.
Installation is the reverse. When popping the bead over the rim, make sure the other side is DEEP in th centre of the rim. Makes it easier to rollover. I often use a small piece of 1/2” plywood jammed in to hold the bead down in the well. Lubricate the bead with the correct tire lube. I use Windex in a pinch.
Your tires may have rotational arrow. Check and check again! If there is a yellow or orange dot on the sidewalk, line it up with the valve stem...... this assumes no inner tubes?
Set the completed assembly in the balancer. Bolt back the disc if you removed it. The heaviest portion rolls to the bottom. I usually tape on the weights until I get it so the wheel stops in different places and if you stop it anywhere, it just sits still...... then peel and stick the weights. If you are using squeeze on spoke weights, same process just tape them on loosely, then crimp them in when you’re happy with the results.