Ground and power PCB layout for MCU
If the part is SMT your best bet is probably to try to put a fairly intact ground pour under the chip (bottom layer) and route most of the traces out of the dense area on the top layer. The power connections can be tied together and bypassed to ground with ceramic capacitors near the chip on the top or under the chip on the bottom. Of course there will be vias near the capacitors either way. 

If it's through-hole, it may make more sense to try to route some traces on top and some on bottom, again with bypass capacitors near the chip. A ground pour on the bottom and a Vdd pour on top may make sense, though neither will be very much like a multilayer power plane. 

Today's circuits tend to have a lot of different Vdd/Vcc voltages, and sometimes Vee if you're doing mixed signal designs, so a complete power plane covering the entire board is a bit of a dream even with 6 layer boards, let alone two layer.