In most cases the problem is that the pattern on the sprinkler nozzle is too wide. With your hand, pull up the popup stem and simply unscrew the nozzle on the top. Bring it in, and we can match it with a nozzle that has an adjustable arc. You can then adjust the arc, making it narrower until you get the desired pattern that doesn't overspray.
Typically this happens on heads that are lower than others on the same zone; it is water in the line draining out of the lowest head. It is only a real problem if the water is running onto hardscapes or it is making the nearby grass thicker or a different color than the rest of the area. The solution is a one way check valve that will prevent the drainage. We carry both check valves that go into the line or a popup body that has the check valve built in.
It is water pressure in the sprinkler line that forces up the nozzles. Either a leak/break in the line or other factor is causing low water pressure that needs to be addressed. If water pressure is good (typically other heads on the same zone are working fine), then that particular head is bad. The body is screwed onto a fitting on the line. Simply remove some soil around the head, unscrew it, and replace.
If you are lucky, this can be an easy fix. Each nozzle is designed to spray a certain distance. You can replace it with a nozzle designed for a longer spray. Not so lucky? Either because of water flow/pressure limitations, too many heads on the zone, poor system design, etc., there's not enough water to properly supply all the heads. Consult an irrigation professional revise the arrangement of heads/zones to match available water flow.
Popups with a taller stem that will rise enough to clear the plants can easily replace the shorter one you have.