I take it this is your first time doing such checks in general.
Not ever single lead is going to be isolated, many are connected to each other through a resistance. A high resistance value (in the kOhms or MOhms) is normal. The definition of a short is when a lead is connected by a low resistance, we're talking about milliOhms here.
To test for these, set your meter to test for the lowest possible resistance. Then touch the leads of your probes together. You should get a small reading like 0.5 Ohms (or 0 if your meter is calibrated to compensate for this). Small changes in resistance is also affected by how you make contact with your probes. If you press them solidly to each other, then you'll get a solid reading, if you allow them to move around, the readings will jump all over the place.
When you touch two leads that are isolated or connected by a high resistance (i.e. not shorted), then you will get an infinite reading (if your meter is set to the lowest setting), the same as if you take the probes off that part. If there is a short, then you will get a very low reading. Small values means low resistance/short, big values/infinity means no short.
The first thing you should test for are cold joints. The most common place for them are on the OP amps, since they have small joints. You do this by placing one probe on the pad and the other probe on the leg of the lead. If you measure anything greater than an ohm, you need to fix the cold joint (usually resolved by simply touching the joint for a second with a hot iron). Then test the resistance between adjacent legs, you should get infinity for all of them.
Also keep in mind that when you measure resistance, you are sending a DC voltage through the part, and the probe is actually measuring the current it receives to test the resistance (this is another reason why you should set your meter to the lowest setting, as if you set it to a high value it will send out a higher voltage to the part, resulting in a higher current, which could damage a part.).
With this in mind, try testing the resistance of a capacitor (mind the polarity, place black probe on the negative electrode). Since capacitors block DC once they are charged, you will notice that your resistance starts low and then climbs until it eventually reaches infinity, since no current will pass. If you try turning the power knob on, you will notice it will flash as the capacitors discharge. Since the battery contacts are connected right to the capacitors, what you are seeing as changing resistance is the capacitors being charged.
Before you check current, test that everything is connected right. A simple way to do this is to insert the battery into the contacts, then remove the battery. Then turn the power on. You should see the power LED briefly light up (it lights up from the charge stored in the capacitors). If that works, then you know you have power flowing.
Current is usually measured by connecting your probe to a different socket on your multimeter (check your manual). Then set it to read up to 200 mA. Connect your battery's positive terminal (make sure the positive terminal is the one near the outside of the board, because otherwise you have installed your battery backwards), but leave the negative one unconnected. You are going to complete the circuit with your multimeter in order to measure the current. You do this by touching the black probe (black probe is always connected to the common/ground on your multimeter) to the battery negative terminal and red probe to the battery contact.
Then turn the power on and keep it at the lowest setting. The power LED should light up as long as the contacts are connected, and the meter should display the quiescent current.
