While there are a number of other designs the two types of fill valves most commonly in use are the BallCock which is on the left side of the above illustration and the Universal Replacement fill valve which is on the right side of the illustration.
The Ballcock is the one most commonly pre-installed in new toilet tanks while the universal replacement type is the one most often used for service and repairs.
If your fill valve is spraying water up against the lid of the tank, first locate the "Trap Primer" line, which is a small diameter tube that should be attached to the top of the standpipe in the center of the tank. During the fill cycle a small percentage of the fill water flows through that and is supposed to discharge down the standpipe to refill the bowl and trap of the toilet. If that line is loose or mis-positioned it can spray water up against the underside of the lid and cause a leak like you describe. The solution would be to properly re-attach the line to the standpipe.
If you have the conventional BALLCOCK type valve press down on the float ball to open the valve so you can see where the leak is occuring. Normally they will leak where the top cover plate meets the main part of the valve body. If this is the case, first turn the water off at the supply valve (The angle stop shutoff on the wall under the lower left corner of the tank).
You can now use a screwdriver to tighten the four mounting screws that hold the top plate on the valve. (If this is an old brass valve the screws may be too corroded to tighten or they may break when you try to turn them. This is why we turned the water pressure off first).
It should not require much more than about a 1/4 turn to tighten the screws.
Once you have the screws tightened you may turn the water on and flush the tank to see if that corrected the problem. Although there are repair kits for those type of valves often it is difficult to locate the correct kit. The cheapest and easiest solution is to replace the fill valve with a universal replacement type such as the Fluidmaster valve illustrated above. A complete replacement kit can be found in any hardware or home supply store for about $10 and it is a simple DIY installation. (The fluidmaster kits have a very good set of illustrated instructions enclosed in the kit.)