How do i run electrical cord or extension across my sidewalk
I can think of three options...

For a temporary solution, you could use a cord protector (those little plastic/rubber ramp things you see at carnivals and other outdoor events). Just put it on the sidewalk, and route you cables through it.

For a semi-permanent solution, you could install a conduit sleeve under the sidewalk.  Just make sure it's large enough to fit the cord ends through.

If you're looking for something more permanent.  You could install a permanent electrical circuit out to where you need it.  This will require trenching, conduit or underground feeder cable, weatherproof boxes, and GFCI protection.