The auto router will do Power & Gnd just fine.
In the schematic, right click a 5V power trace and give it a net class property of Power or whatever you named it.
Draw a polygon around the outside of the board, will look like a dotted line. Right click & name it GND. When you click Tools:Rats Nest, it will fill in open spaces and connect grounded signals.
If you're going to send the board out to be fabbed, go ahead and make it double side, since the material starts out as double sided copper clad fiberglass anyway as standard stock.
Draw a GND polygon on both layers, outside of the board boundary so you can see it easily.
Then you can also select Rip Up and single click it to hide it and see your traces easier.
For better autorouting, select View:Grid and select mil.
Then under Tools:Autorouter, select 2 mil for the routing grid, that should get a lot more of the routing done assuming you had decent placement to start. You may have to add some Vias named GND to help with the last ground connections.