Cleaning the climb
Penn State, it might help to talk first about getting past that rock, and then about climbing in general.
To get past the rock,
- accelerate before reaching it, then stop pedaling and get your cranks level.
- get off the seat, and bring your upper body low and well forward, up over the handlebars.
- let momentum carry your front wheel over.
- (the back wheel is now reaching the rock) use your arms, shoulders and back to shove the bike forward under you, to help the back wheel up and over the rock.
- make a stong pedaling stroke as the rear wheel gets to the top of the rock, to help get the bike up and over.
This is sometimes called a "lunge", and on level ground you can practice moving the bike back and forth under you to get a feel for it.
Whether climbing or on the level, we sometimes create a problem for ourselves just by reaching the critical point of passing an obstacle, dip, etc. with the pedals in the wrong position. The worst position at that moment is 12/6 o'clock, because we'll be delayed a full quarter-revolution until we can apply some power to the situation, and by then it may be too late. It's much better to coast briefly with the cranks level so we're ready. Sometimes, in a tricky spot where coasting isn't enough by itself, it can pay to "ratchet" (spin the pedals backwards a bit) to get the cranks level so we can add some leg drive an instant later when we'll need it.
About climbing generally,
The best position is to bend forward at the waist, bending your elbows and lowering your head and chest toward the top tube. To help deliver traction to the rear tire and keep the front tire on the ground, pull back (not up) with your hands as you pedal.
If you stand, keep the same position - bent at the waist over the top tube.
Perhaps the biggest self-inflicted cause of a lack of traction during a climb is irregular pedaling. If the power comes on in bursts the back wheel will tend to break free. This is a particular problem when standing up because we can generate more power, and standing strokes are naturally more choppy. It can help to be in a higher gear when standing during a climb, because the greater resistance smooths out the pedal strokes. This approach is especially useful when the surface is loose or muddy.
Alternating between standing and sitting during a climb can also cause irregular pedaling. Once standing, it may be best to stay up until the grade levels out a bit and we can sit down again.
BTW, if you're sliding off your seat, you might want to lay a board on it to make sure it's not tilted back. You can also try angling it nose-down slightly to see if that helps.

...and never Armor-All your seat...
