x86 CPUs on your normal PC platform do not implement scheduling in hardware, it is the kernel's job to do that. Neither do any other common CPUs such as ARM, MIPS, PowerPC, etc.
does the hardware normally provide instructions to help with scheduling such as for loading or storing the registers at an address in memory?
"Loading and storing registers at an address in memory" is a fundamental CPU operation that helps with just about everything a CPU does, not just scheduling tasks.
And not really - continuing with x86 as an example, there aren't any special process scheduling instructions.
About the only thing required from hardware from a scheduling perspective - if you want to have a pre-emptive multitasking system as opposed to a cooperative multitasking system - is a way to interrupt a task that is taking too long, and the PC platform provides timers that cause interrupts when they expire as a way to force a process to relinquish control of the CPU.