Hi Gordon, You've not said which model grass trimmer you've got so I'll try and answer your question on the assumption that it is fitted with a two-stroke engine (the type that you have to mix oil with the petrol)
I'm also going to assume that you're trying to start your trimmer for the first time in a while (and not on the basis it was running yesterday and all of a sudden it's stopped working)
The first thing to do is to empty the fuel tank of any old fuel, fill it halfway with fresh petrol only and no oil. Cap off the fuel tank and give it a good shake and press the priming button a few times. This will flush out the fuel lines and clean the tank to a certain degree. Then pour out this fuel and dispose in a safe manner. You will then need to clean the carberettor, as old fuel and oil will leave a gummy deposit inside that will stop it working properly. It's best to use proper Carberettor Cleaner spray for this job, following instructions on the product can. Finally you will need to make sure the air filter is clean. When this is all done and you are satisfied that the fuel lines, carberettor and air filter are all clean, fill with fresh fuel and oil mix and it should fire up.
The trick is to be aware that a small two stroke engine needs to be emptied of old fuel and flushed through before storing for the winter.