One of the benefits of sharing the Swords & Wizardry PDF via email last week was the number of connections I made with other gamers. God knows I've fumbled my roll to answer everyone back, as the initial response was, to say the least, overwhelming.
One interesting email asked me about "skill resolution" in Swords & Wizardry and what method one would use. Now, to be honest, I kinda "wing it".
I loosely base such things, like a chance to know some obscure knowledge, or find something like tracks, on a Saving Throw adjusted by relevant stat bonus. The number needed to be successful is adjusted up or down by up to 3 pts, depending on ease or difficulty. Additionally, bringing the right tool to the job (like an iron spike and a hammer to bust a padlock) will adjust the target number in the PCs favor, while the wrong tool (a random rock) my incur a penalty to the target roll.
All of the above is a long winded way to justify a Saving Throw target number that "feels right", which in my mind is much of what the OSR stands for. It's not just DM empowerment - "trusting the DM to improvise gameplay resolution on the fly" but it's also a manner of play that empowers players - "You mean I'm NOT limited to a selection of skills and feats on my character sheet?"
As an "old school" DM, you use a formula like I spell out above until you get a feel for doing it on the fly, because keeping momentum going in game is more important than being exact on the numbers - keep it flowing and keep it fair and your players will keep coming back.