Is it covered in spider webs, is the the chain rusted, are the tires flat, are there any obviously missing parts? These are basic things you want to be looking for as the bike sits in front of you.
The wheels should be straight in the dropouts and inline with the middle of the frame and fork. If the wheel isn't straight relative to the frame, make sure it is straight in the dropouts and re-check. If it still isn't straight, either the frame or fork is bent or mis-aligned.
Condition of wheels
Pull the rim/tire lightly from side to side. You're looking for any play in the hub bearings. If the hub bearings are within tolerance, they shouldn't move. If you feel a click or klunk, the hubs need to be adjusted or re-built.
Spin the wheels and look at the rim in relation to the brake pads (for rim brakes) or fork blades/chainstay blades for disc brakes. The rims should be true without wobbles or bulges in the rim surface.
For rim brake bikes, look at the rim surface. The braking surface should be smooth and not overly concave. There is some tolerance, so consult the rim manufacturer for wear tolerance information. It is important to monitor your rim's wear because the rim bead could let go, causing a very dangerous situation. You'll need to rebuild the wheel with new rims if the rim surface is too concave. You can check by putting a straight edge against the rim and seeing how worn it is.
Are the tires flat? Could need new tubes or rim tape - you won't know until un-mounting the tire and doing an inspection. Try inflating the tubes and seeing if they hold air. Tubes can lose air over time, so a flat tire can be due to a puncture or it could just be due to time.
Check the overall condition of the tires. Check for abrasions, dry rot, lumps, and debris. Be careful spinning the tires and placing your hand on it. I've gotten cut by an errant staple in the tread, when spinning a tire to inspect it.
For rim brakes, check to see if the pads have equal distance to the rim. Squeeze the respective brake lever a couple times to make sure they haven't been knocked about and re-evaluate.
Dig your fingernail into the pad and to see what condition the pads are in. If it feels fairly pliable and soft they are good to be adjusted and re-used. If they feel rock hard, replace them. When in doubt, replace your brake pads.
Disc brakes are a bit harder to diagnose as they are harder to see within. A flashlight would be helpful to see within the caliper. If the bike has hydraulic brakes, check the junction points at the lever and brake caliper for any leaks. Here's a picture of a fresh vs worn disc brake pad.
Now give each brake lever a squeeze and try pushing the bike forward. Obviously if the brake works, it will be difficult to push the bike forward. If the bike has disc brakes and can be moved easily, then something is very wrong. The pads and rotors could be contaminated with grease or oil, or there is a leak in the hydraulic hosing, the cable/housing needs to be replaced, or the caliper needs to be re-built or replaced. Either way, it will need to be diagnosed when it's in the stand and disassembled.
While you're grabbing the brake levers, let's check the.......
Grab the front brake lever and rock the bike forwards and back. If the headset moves, it will need to be adjusted or rebuilt (depending on how it is made). Some disc brake pads move within the caliper (which is normal). You might need to turn the handlebars 90 degrees (wheel to the side) to isolate the headset from the brakes.
First, check the chain for rust, stiff links, gunk, and correct length. You probably don't have a chain measuring tool at home, but if the rest of the drivetrain looks to be in decent shape, you can probably roll with it.
Check both the front and rear derailleur for smooth operation. This is best done in a bike stand, but in a pinch you can hang the bike from a tree branch, a broomstick between two chairs, or some other creative perch. Turn the crank as you shift through the gears. The chain should move freely from one gear to the next. You'll also want to make sure the chain does not drop off the cassette or chainrings at the highest and lowest gears.