I crewed on a racing team for about 10 years and we did our alignments by hand. You still need some equipment though, especially to do Caster.
We would create a level surface by building up three of four spots the car sat on with linoleum tiles on a fairly level part of the shop. The tiles worked real well under the front wheels for checking Caster because the tiles would slip on one another as the wheels were turned.
We used a Snap-On alignment tool that was hand held. We had to make an adapter for the wheel hub. The alignment tool was magnetic on the end and the adapter would snap onto it. You held the alignment tool to the wheel hub to check Camber and Caster. As I said, the wheel would have to be turned to measure Caster.
Toe was done with strings and a scale measuring off the rim of the wheels. Jack stands were used to support electrical conduit running in front and back of the car. We cut notches in the tubing so the strings would stay both stable and parallel with each other. The jack stands were used to get the height of the strings as close to the centerline of the wheels as possible. The conduit could be moved side to side to get the strings equidistant and parallel to the car measuring off the hubs using the adapter mentioned above removed from the alignment tool. We just used a pocket scale from the adapter to the string.
Then, you could measure toe off the leading and trailing edge of the rims.