The Wanderlost video is good. However, I would do one thing they didn't mention. Whenever I do brakes I take the top off the master cylinder and then set it back on without hooking the bale. Doing this makes it easier to push the caliper pistons back in to make room for the new pads.
I usually use the old pad and either a pair of channel locks or a c clamp to push the piston back. This will push fluid back up the lines and into the master cylinder reservoir; so go slow so brake fluid doesn't spill out of the master cylinder because of the loose top.
Inspect everything: condition of the fluid, piston seals, line connections, etc.
If any brake fluid spills clean it up pronto. It will eat through paint in a heartbeat.
If you have a bad piston seal, it will obviously have to be replaced before you can continue. The hard part is getting the piston out of the caliper; as it's a tight fit around the seal. If you pry on it and scratch anything, it will cause a leak. Here is one way to get the piston out without damage. It will require removing the caliper from the vehicle.
With the caliper on the bench place something soft (like shop rags) in front of the piston. Then use an air hose with a nozzle to blow air into the hole the brake line screws into. The air pressure will force the piston out. Install new seal lubricated with brake fluid and then push the piston back in. You'll have to bleed the line after reinstalling the caliper. May end up having to bleed all the lines.