If you had a climbing rope anchored above you on either a sheer cliff or a really steep incline, what is the minimum amount of gear that a person would need to ascend the rope without assistance from above?
There are a few options:
No gear: Actually even with a free hanging rope you would not need any gear (assuming you can hold your own weight with just your hands) using the russian wrap. It does however take some practice.
Harness + Prusiks: If you want to do it safely, you should use some kind of harness. You can use a commercial climbing harness, or e.g. tie a swiss seat from webbing. Then for ascending the minimal version would be two cords about half to 3/4 the diameter of the rope you intend to climb, using the prusik hitch to attach them to the rope, and tying them to your harness.
At least one of them then should have a long enough part to make a foot loop. That way you can alternate by weighing your harness and weighing the foot loop, and shift the other prusik knot upwards, and you're safely connected to the rope itself.
Another way is only connecting one prusik to your harness but still using the other one for your foot loops, known as Texan Prusik
If you also want to do it efficiently, it might be worth investing in some more gear like carabiners, slings and mechancial ascenders, see e.g. Fixed line: Prusik vs mechanical ascender
No gear #2: If there is enough rope, you could tie a simple harness in the end of the rope (e.g. again using the swiss seat, or the one-loop harness) but still leaving enough tail to tie it with a Blake hitch to the standing part of the rope (the part going upward to the anchor). This acts like the harness-prusik. Then instead of a foot prusik you could again use the russian wrap.
Shoelaces... At least according to James Bond.