This is easily the biggest design flaw with this console, the shoulder buttons love to break off and tear the copper pads out. Hold it up to your ear and give it a shake. Hear something rattling around inside? That's your L button.
First step is to assess the damage. Take the motherboard out and look for the button mounting point. If all the pads are there, great! (also, you're very lucky). Just solder in a new button and you should be good.
If you're not so lucky and some (or all) pads are gone, it gets trickier, and you'll have to scratch some of the solder mask off to make new contact points. You can do this right next to the pins, and solder directly to them, or pick a point further along the trace and connect it with some trace wire. The two side (ground) mounting points, though, provide most of the structural integrity and should be connected directly.
The button is the same one used in other 3ds models + joycons, and can be found with a search like "3ds replacement shoulder buttons".
As for tools, you'll need the ones listed in the motherboard guide, as well as some form of soldering setup. Doesn't necessarily need to be fancy, just enough to attach that button. It's doable with a fine soldering iron, but maybe easier with hot air. (Can't be sure, i've never used hot air)
Good luck! We're all here if you have more questions