You can climb vertical surfaces that are not smooth (that have enough holes and/or protrusions to use as handhold). If you do not have explciit climbing speed, you can climb for half of your normal speed (for example you can only climb 15 feet if you have movement speed of 30. Rounds up). You cannot dash-climb (dash action only works on horizontal movement).
While clinging to a vertical surface, your hands and feet are used to hold yourself up. You cannot perform any actions that require them (for example you cannot cast spells with somatic component).
Before every [your climbing speed] ft of climbing (including at the start) you have to make athletics check. If you fail, you let go from the surface, fall to the ground and fall prone (you do not fall prone if you fell from less than 5 ft). You cannot climb again this turn. DCs for various surfaces:
Climber's kit works similarly as described in the official rules. Clarifications and changes:
If your characters holds the rope at the top of the cliff, you must make Strength check every time new person starts climbing on your rope. DC is (8 + number of people already on the rope * 3). If you fail, you let go of the rope. If multiple people hold the same rope, all rope holders roll the check and you sum the result. If one of the rope holders lets go of the rope, the rest of the holders must immediately re-do this strength check.
When holding the rope with people on it, you can use your action to pull the rope up. Roll D20. You can pull the rope up by
((Dice result + strength modifier) / 2 - people on the rope * 3, rounding up) ft. If other people also hold the same rope, they can spend their reaction to help you pull rope up. They make the same roll and you sum the results. If any person rolls 1, that person lets the rope go (he can take hold of the rope again as action on his next turn).
If rope is also attached to the anchored piton, use the same rules as if piton was the person that holds the rope and always rolls 8 (with +0 strength). Piton can't help moving the rope up.
When falling onto snow, you reduce your fall damage as if you fell by 15ft less.
Do not forget: Objects also have HP (https://roll20.net/compendium/dnd5e/Objects). If you throw down an object to your ally and that idiot does not catch it, it can get damaged or even destroyed by the fall damage. Be careful with your magical items ;)