Check connectivity:
1) Print schematic.
2) print each layer of PCB
3) obtain lightbox that paper fits on (can be done without - but this is better) - unless you can print it out in colour - different colour per copper layer.
4) Get box of highlighters.
5) Start following schematic and checking the components have been placed on pcb, tracks are connecting them right.
Highlight done connections on schematic & pcb.
Use yellow for OK, Red for wrong.
When finished - fix the red ones and recheck those areas.
Had you used the schematic to make the PCB, using the software and a rats nest then you could use the software to double check the connections.
Check against design rules:
Setup design rules in the pcb for track to track, track to pad etc.
Run a DRC/design rule check in the pcb program.
Review each error found and fix them.
Check silkscreen:
Your PCB package may not include silkscreen over pads checking so turn on only the following:
top electrical layer - pads (component and testpoint), silkscreen layer, names/outlines/text etc.
Review every square cm of the PCB checking and moving silkscreen items so that they do not cover the pads.
Perhaps let people know what software you used and we can advise you further.