My UV filter is looking pretty dirtyand I'm not sure what to clean it with...

Wet the filter first under the faucet, gently wash the filter with a soapy fingertip, rinse, repeat until all the residue is gone. Shake it dry, dab it dry with a soft cloth, then polish any water marks off with a microfibre cloth.

I bought some used filters online that looked like crap and this did the job for me.

Be extra-careful with CPL filters because water can get in-between the elements.

For the lenses, a quick blast of air to remove dust and loose debris, and I'll follow up by breathing on the front element and wiping with a lens cleaning cloth to remove whatever might be left.

or courdaroy pants, if I happen to have them on