I'm looking at getting some tools that will require having 220 for them. My main panel is full right now and has several Slim/Tandem/double breakers in it already. Reading some things on the net I see that the panel might be exceeding the limit it should have for breakers, but don't know at this time of writing.

I'm looking at adding a sub-panel, but of course I'd need to remove some circuits to do this and move those into the new sub panel. My question is how to do this when the wires are already in the main panel? I wouldn't think you could wire-nut an "extension" to sub-panel that is right next to the main panel.

Thanks, Michael

I would consider Larger Panel, than adding subpanel. Unless you need more than 42 circuits.
You can wirenut in panel and move to next panel.
If you do move circuits. Most are straight forward, The one most important, is 2 circuits
Sharing 1 neutral. Usually 1 Red, 1 Black, sharing 1 Neutral(White), They need to be on opposite phase. If not, Neutral will carry a total of 2 circuits, instead of difference of the 2.
20 circuit Neutral could see 40 Amps(#12 only rated for 20Amps)