OSHA - How often an employee needs to be Re-Trained on Safety Methods

Can someone point me to an OSHA document that states how often an employee needs to be re-trained on safety methods? Does this document even exist?

I've had people in my company state that OSHA mandates annual safety training. If they do fine, but please show me where it says so.

You could start here, but you might not ever finish reading. There are a lot of OSHA standards. Here is a summary of training requirements published by OSHA: Training Requirements in OSHA Standards. It's still 270 pages. I'd try searching it for "annual," "frequency," "retrain," "refresh" or similar terms to find what you need. Or you can just look at the topics you're interested in.

You'll have to check specific OSHA regulations that govern your specific needs under 29 CFR 1910 (General Industry)

There is no one single answer to your question

I can tell you what my Corporate Safety policy requires for annual training for every employee, if that helps.

Safe Lifting/Back safety
Fall Protection (as applicable)
Emergency Evacuation Plan/Firedrill
Fire Extinguisher training
Hazard Communication Plan/GHS symbols
Lockout Tag Out
Machine Guarding
Cranes, Chains, Slings and Hoists
Confined Space Entry (as applicable)
Bloodborne Pathogens
Rail Safety (as applicable)
PPE
Outside Contractor Safety
Powered Industrial Truck (Forklift, Side Loader, Aerial work platform)
Hearing Conservation (as applicable)
Respiratory Protection (as applicable)

Forklift Operators - 3 year certification & annual refresher
First Aid/CPR/AED training -2 year cert, min two employees per shift.

We use JJ Keller for training videos and content, they do a great job.

When we were under private ownership, we treated it as on the job training and didn't place a huge emphasis on it. There was a prefab manual from Paychex that hit the documented requirements but honestly, it sat on a shelf.

As randy stated there is no single answer to this. However, given the importance of safety, I would at least annually. We do a general safety video as part of our new employee orientation then cover various topics on a monthly basis. Sometimes based on an incident (thankfully rare) but most times just something that comes up in our daily huddles. The point here is to simply keep everyone focused on safety.
That said, there are things (such as Lock-out Tag-out) that do have retraining requirements attached.
Good Luck.