How do I unclog my bath tub drain?
As mentioned by Ecnerwal removing the over flow cap is the easiest way to snake a tub. Most 1/4 inch auger drain snakes have a 25 foot cable. If just the tub is not draining and the sink in the same room is draining correctly that tells you the clog is not to far in the tub drain (since both drains connect to a main drain pipe).
Snaking to clear a blockage in a pipe takes acute sensory perception. Knowing if the snake stopped advancing because of a fitting or the clog is a skill.
Try the snake again through the over flow drain. Extend the cable the full length. When you meet resistance ream the snake back and forth several times. When you retract the cable note what (if anything) is stuck on the auger tip.
When executed properly there will be a noted increase in (or complete) draining. You may need to re-snake several times depending on the type of blockage. Once it is cleared run hot water for a few minutes to remove residual clog and caustic drain opener. You must be careful when working with water that has chemicals from a drain opener still dissolved in it. Don't let the snake splash any water on your skin or face.