How do I rewire a switched receptacle and make it permanently hot
The 2 black wires are piggy-backed, indicating that one is the incoming hot and the other is the hot to other device(s). The red appears to be the switched hot supplying the receptacle in question, so...

Turn off the power at the circuit breaker/fuse panel first! Then disconnect all the wires from the switch and connect them together with an appropriately sized twist-on wire connector, except for the ground, which simply terminates at the box. The red wire supplying current to the receptacle will now be an un-switched hot.