Make sure everything is turned off before you remove the battery: radio, climate control, etc. You don't want any power surges going through those later. That's about it.
The seat just lifts out (grab from underside of front edge). You might have to give it a firm jerk. Don't be shy -- you can't hurt it. It just lifts out.
The breather hose just pulls off. If you are careful, you can remove battery while otherwise leaving hose in place (just gently push it aside while unloading battery and loading new one). Likewise, when the new battery is installed, hose just pushes back onto the new battery's vent port. Make sure it is on all the way.
Disconnect red battery cable first, and tuck it away so it won't spring back and touch the wrong place. Then the other one. Then swap old battery for new. Reinstall cables in reverse order. Put some dielectric grease over the battery cable bolts right before screwing them in. Just a dab; and spread it over the threads a bit. This keeps moisture out of these important electrical connections. You can buy a tiny tube of it (about four inches long) at local auto parts store.
Don't over-torque retainer bolt during reinstall. Don't want to break the plastic. It should be firm, but does not need to be super-tight. Note how tight it is during removal and try to match that.
Pay attention to inner seat belts when reinstalling seat, so they don't wind up underneath it. Position seat down and rearward, then push down firmly along the front. A gentle tug upward will tell if it's locked in or not. You might have to try it 2-3 times before you figure it out, if you've never done it before.