The Run/Stop switch for most of the old McCulloch saws will be forward to run, back to stop. Remove the spark plug and make sure you have a spark in the run position, if not try the other way (back) but chances are if there is no spark you will have to remove the flywheel and clean the points.
The 300 should have a Tillotson HL carburetor, and the right hand button with the screw sticking up is the choke. Push it in and twist it to the left to lock the choke on. Remove the air filter cover and air filter and verify that the choke plate is completely closed; if not you will have to tweak the linkage a bit to make sure it closes fully with latched on. The button on the left is the manual oiler, the 300 does not have any automatic oiler function so be ready to pump the oiler every few seconds while cutting.
If the saw has not been run in a while, it may be helpful to put a little fresh mix directly in the carburetor to give it a prime. Assuming the carburetor is not gummed or plugged completely, it might take 2-3 or more primes before the saw starts to pull fuel on its own. If you prime it and it pops and runs the prime out more than 5-6 times without running on its own, you are probably due for a carburetor kit, check the fuel lines (inside the tank as well as from the tank to the carburetor) while you are at it and the fuel filter inside the tank as well.
Mark