On ability scores, skills, and chances for success

Usually I just go with my gut, lay out the situation for the players, and tell them the chance of success. Most of the time this involves d6s. They have low ability mods like OD&D (>8 -1, 9-13 +0, 14-17 +1, 18 +2) so in extreme cases, when I really think their skill in a particular area will matter, I let them add their modifier to the roll. Not often though. Mostly I just glance at their character sheet and arbitrate "Oh, you've got 16 in Dex you could totally use your 10' pole to help you jump this gap" or "You're a halfling wearing platemail, you gotta try something else." If they demand a chance to roll for doing something stupid and impossible I'll let them throw for 1 in 6.

Risk/reward is the answer for coming up with rulings. Is there a risk? Is the risk interesting? Would it be MORE fun if they just succeeded? They've got the gear, they've got the time, they're competent explorers, there's no reason they can't just climb a short cliff in twenty minutes or so. If they're trying to climb gearless while goblins are shooting at them, that's when the dice come out. If they want to climb up an insane height I might throw in some complications along the way to spice up the "yeah you just do it". Players like to succeed, and accomplishing things inspires them to try new things. If you're forcing them to take a chance at failing basic adventuring tasks they're not going to feel empowered.

It doesn't need to be codified because every situation is different, and bean counting modifiers in the middle of a dangerous situation is the best way to kill momentum.

Thieves are the only ones that pick locks, but it takes time. In a pinch they can roll to see if they do it quickly. "You wanna pick that lock? It's kind of beat up and rusty, and a weird design you haven't seen. It could take a whole hour, are you willing to risk 3 wandering monster checks?" or "You hear lizardmen clanking around in the tunnels behind you, they're getting closer. Roll d6 and add your Dex, if you get 5 or better you succeed, if not they're gonna be right on top of you."

It all comes from the fiction. They want to sneak past a doorway guarded by two orcs. Orcs can see in the dark but they can't. They have to put out their torches and feel their way, under cover (maybe there's stalagmites or some shit to hide behind), to where they're trying to go. Or maybe they'll change their plan to involve a distraction. If they decide to sneak, along the way I'll throw dice, d6 d10 or d20 depending on my mood, but just as often 2d6 a la Dungeon World, and riff off of that. If they get a bad roll at the climax of the situation something bad will happen, like the Orcs hear a noise and come looking. Maybe they change tactics in the middle, or the thief Merges with Shadows and sneaks behind them, or the Wizard uses an illusion to turn himself into another Orc and come up with some goofy lie. Mostly, though, they just sit there and go "uhh uhhh uhhhhh..." until I decide they've had enough time to think and the orcs are here now because my players are idiots.

If they wanna sneak past unsuspecting people in a non-monsters situation, I'll just let them do it if they tell me how they do it. If they're trying to do something risky other than just being quiet and slowly moving through the underbrush, say they wanna open the witch's door and slink up her stairs while she's busy at her cauldron, I'll tell them "That's risky, the witch is pretty observant. Are you sure you don't want to try to climb up to the second floor window or something? Okay, well you already took off your platemail. It's 3 in 6 you'll get by and up the stairs quietly. Roll it." Why is it 3 in 6? Because 1 in 6 is too small, and 2 in 6 seems unlucky. A 50/50 shot feels just about right. No other reason.

Think about it, how easy is it to hide in any given room? Look around the room you're in right now. If someone was trying to kill you, and knew you were somewhere around, they would probably find you unless you had a great plan for how to get out of the situation. How boring is it to force them to fail at picking locks? Hell, I hate failed rolls "you miss" so much I usually use it as an excuse to throw in complications "You miss the fire beetle and also now it's next to you and has a good bead on the elf, elf you see him coming at you what are you doing?" If they're willing to spend the time doing some dumb shit just roll to see if monsters show up in the middle of it. That's all the punishment and partial results they need.