Proper positioning is the marksman-counterplay for dealing with assassins. If you have to push a lane to siege their turret, make sure you're in close proximity to a teammate who can shake them loose with a CC/displacement or heavy burst damage in case said assassin tries to all-in. Orb-walking--or moving to reposition in between autoattacks--is also a pretty essential skill. Some marksmen also have autoattack-resets or skills that can be weaved in-between autoattacks--all of it is important and the sooner you get familiar with it the more you will improve!
Always focus the highest-priority target you can safely reach without getting jumped on. Sometimes this is going to be a tank--in instances like these, it's extremely important to keep your spells/abilities on reserve and save them for when an enemy squishy sticks his neck out to make a play. Outside of that, it's all about balancing risk vs reward and deciding when to go in for the all-in.
Above all else, play the bot marksman role a lot. It takes a lot of practice to carry an entire team with a glass-cannon but obviously not outside the realm of possibility--keep practicing!