I'm not sure just what "level" your problem is on... You can't "mov [mem2], [mem1]", of course - you have to move memory contents into a register, and then move the register back into memory. Or movsb/movsw/movsd will move a byte/word/dword from [ds:esi] to [es:edi]... You can push/pop from/to memory, too...
When it comes to displaying memory - or displaying anything - it matters what OS you're targetting. With a "protected" OS, you won't be able to access memory you don't "own", which might be a problem, too...
Maybe if you post the partial program you've got, or tell us what you've tried that doesn't work, we could be more help...
Best,
Frank