I got a kit that came with a lot of cool components, but had no way of using some of them without a soldering kit. As necessity is the mother of invention (or lack of tools is the mother of improvisation), I discovered a (temporary) workaround, using only a spool of solid 22-gauge wire, a wire stripper, needle-nosed pliers, and the right combination of boredom and free time.
Step 1: Gather Materials
Wire (whatever fits the 'thing' you're connecting)
Step 2: Cut Wires
I find it preferable to have some length to work with. Cut however many pieces of wire you need, whatever length you need. They were too short/uneven to work with my first try, so I had to start over.
Step 3: Strip
Remove enough on one end to fit through what you're connecting. For this LCD panel, I only had to take off about 3 millimeters. I was connecting the other end to a breadboard, so I stripped off about 3/4 of a centimeter. (At least that's about all I needed to strip)
Step 4: Connect
Insert the wire, bend it into the hole, use the pliers to pinch the wire in place.
Repeat as needed.
Step 5: Utilize!
I used this on a LCD display with an arduino. I'd say it works!