It's hard to tell whether your crank is a classical design or something new and weird. For the classical design you use a "crank puller".
These look sort of like what you show, but you notice the "barrel" is threaded. You remove the bolt holding the crank on (using a standard "Allen" hex wrench) and then thread in the outer barrel of the puller, into the female threads surrounding the bolt head. Turning the arm (or using a wrench on the inner part) then "pulls" the crank off.
Some cranks are "self pulling". You leave in place the dust cover over the bolt, insert an Allen wrench into the hole in the dust cover, then unscrew the bolt against the dust cover.
If your crank is not the "classical" style then you will need whatever specific tools the manufacturer calls for.
Once the crank is off, of course, you may want to remove the "bottom bracket" cartridge. There are about 6 different wrenches for this, for different styles.
Park Tool has an excellent web site with instructions on how to do all this stuff.