Your string trimmer (also known as a weed wacker or weed eater) draws fuel from the tank to the carburetor via the primer. When the primer won't prime, the engine won't run.
Primer Bulb and Line
The primer is a small plastic bulb with an attached line that feeds the string trimmer fuel. Pressing the primer a few times before starting will deliver the fuel. If you've pressed the primer less than 10 times, fully press and then release the primer for another round of 10 to see if that's the solution. If not, the bulb may be damaged.
The bulb and line can become clogged or tangled. Check the primer bulb for damage, as cracks or holes can appear in the plastic over time. If the bulb is intact, examine the visible line to ensure it's not tangled or pulled. The primer is used for "cold" starts, so if you're running out of fuel or if the primer is being used after warming up, the carburetor or fuel line may be damaged and in need of service. Primer bulbs that are cracked can be easily and cheaply replaced.
Check Gas Tank and Seals
Is your gas tank properly filled? The contents of the tank shouldn't be more than 90 days old. Draining and replacing the existing fuel with a mix of fresh fuel and two-cycle oil (one gallon of fuel with three ounces of oil is the rule of thumb) may solve your problem. The seals around the gas tank need to be examined for damage as well. The gas vent should be open, and the oil and fuel should be mixed. Shake the tool to mix the oil and gas if it has been several days since refilling since the two components can separate. Be careful not to flood the engine.
Check the Carburetor
The carburetor is located near the choke and primer bulb. The air filter or muffler may cover the area. Use a screwdriver to remove the cover to inspect the carburetor. There are two fuel lines that connect to the carburetor. These can become blocked. Gently pull off the two fuel lines using a pair of needle-nose pliers and hold the trimmer upside down. Are there drops of fuel coming out? If not, fuel isn't reaching the carburetor, and the fuel lines will need to be replaced. If the fuel lines are intact, the carburetor may just need to be cleaned of buildup. If cleaning doesn't solve the problem, the carburetor may need to be replaced. It's cheaper to buy a new carburetor than a new string trimmer.
Replace Fuel Lines for Primer
Safely drain all the remaining gas from the trimmer tank into a fuel container. Once it's empty, use your needle-nose pliers to pull out the fuel line and fuel filter from the engine. A new fuel line and filter can be bought at your local home improvement or hardware store. When purchasing, make sure the replacements fit your brand. Replace both following the instructions on the packaging. When finished, refill the gas tank, reconnect the primer line to the carburetor and press the primer. The gas should flow into the carburetor, allowing you to start the engine.