The Spitter is the first enemy in the game that primarily attacks with projectiles.
Spitters will attempt to get close enough to Albert West to hit him with their ranged attacks, which has about the same range as a pistol and a very slow travel time, as well as a slowing effect if it hits. Once close enough, it won't approach any further, but won't back away from West, either. If West is in melee range to a spitter, it will attempt to claw at him twice; this deals some damage, but is relatively slow.
A pistol can be useful to pick off the spitter's health, while you stay at a respectable distance so that you can react to its shots more easily. Alternatively, if it's alone, strafing around it while bashing at it with anything will suffice. It shouldn't take too long to kill either way.