Lift the bike lightly by the saddle, should show any play in the bushes. Grabbing hold of the swingarm and trying for side to side movemnet as well.
Hold front brake on and rock bike to check the headset but this will also show play in forks. You may need other person to rock while you lightly feel the fork legs against the sliders for movement.
Check the sliders for any big nicks or scuffing. If there Fox's Mojo will have a party with your credit card to service them.
If it's more than 18 months old and been ridden a fair bit chances are it would need the bearings looked at in the rear.
Grab crank arm and try and pull away from the bike, this will show any BB play. Same with wheels, check for any lateral play or lift and spin them to hear grumbling bearings.
Buy a chain checker as well and measure the chain.