A small Phillips #0 and a plastic spudger will do it.

You probably already have both. The real issue is opening the case without scratching the plastic — that’s where the spudger (or a guitar pick) earns its keep. Anti-static? If you’re just swapping one stick, touch a metal sink or table leg before handling the module. A wrist strap is overkill for this job.

Most ultrabooks that still have socketed RAM use a tiny Phillips head screw for the bottom panel. Once that’s off, the RAM is usually held in by clips you push outward with your thumbs. No special tools beyond that.

Don’t force anything. If the RAM doesn’t click in easily, check alignment — the notch is off-center. If the screws are stripped (common on budget ultrabooks), a precision flathead can sometimes work, but replace those screws when you can.

Future you might appreciate a magnetic tray to keep those tiny screws from vanishing into the carpet.