For new readers, Into the Depths is a one-page D&D-like inspired by Searchers of the Unknown that I wrote over Christmas break. It's compatible with most Swords and Wizardry material. You can download it for free here. I'm going to eventually write a magic supplement for it, but in the mean time I'm using Wonder and Wickedness as the spell system.
Into the Depths uses a fairly simple skill system. Any time you try to do something with a risk of failure and a consequence for failing, you roll a d6 and try to get a result of 5 or higher. If someone helps you, you roll a d8. If you're "Good At" doing the thing in question, you add +2 to your roll. If a group is doing something that they all succeed or fail on together, then they nominate someone to roll on their behalf.
The "5 or higher" is basically a DC (a "difficulty class" from d20) and can be adjusted up or down as you desire. I mostly only adjust it up, while things that make the task easier add bonuses to the PCs' rolls, simply to keep it all as simple addition. Most equipment typically doesn't add bonuses, it either allows you to do things you couldn't otherwise or allows you to avoid having to make rolls by automatically allowing you to succeed (a few pieces allow you reroll a failed roll).
One of the things this system is intended to do is to give the PCs kind of a crappy initial chance to do anything (unless it's an area of core expertise) and so encourage them to grub around for bonuses to their rolls. Here are some of the ways that I let them do so, that you might want to try in turn.
+1 to rolls for:
Taking double the usual time to complete the task
Having a clue, secret, or other inobvious but relevant information
Someone else has done the hardest part of the task
Having a specialised piece of equipment (Specialised equipment should only apply to a small set of predefined situations)
Magical assistance, including blessings
Executing a plausible, well-described plan of action
+1 to the DC for:
Each person past the first two in a group where one person is rolling on behalf of the group
Rushing (1/2 normal time or less)
Plans relying on seriously flawed or incorrect assumptions
Difficult environmental conditions
These lists aren't meant to be exhaustive, they're just prompts to get referees and PCs alike thinking about how they can fiddle with the difficulty of any given challenge.