It looks like you have a screw-on cap on your drive side crank, and a pry-off cap on your non-drive side. Unscrew the drive side cap with an allen wrench, pry off the non-drive side with a screwdriver.
If you intend to open up your bottom bracket, you'll need a crank puller. Park tool makes two crank pullers. I suggest getting the CCP-2, which I have used many times without issue.
I have use a sugino lockring wrench to undo lockrings in the past. It has a single tooth and can thus be used on lockrrings with any number of notches.
+1 on the freewheel tool. Get a fw tool with 2 teeth instead of 4. A 2-tooth tool can be used on a 4 notch and a 2 notch freewheel.
Most lbs's have a whole rack of park tools.