Here's a chair before we did anything.
As you can see, this furniture set needed a lot of work. So that's what we did. We started by sanding all the visible wood. The "proper" way to refinish a piece like this is to take off all the wood, work from there and then reassemble the furniture after everything is done. However, with fear of breaking the furniture past repair, we stuck to not taking any of the wood off.
This is after we sanded the chairs. It already looks so much better than when we purchased it for sure. Now, since it was sanded the wood will soak up the stain nicely.
You can see here that the stain looks really nice and the chair keeps on improving. We did this to all of the pieces (obviously, so they match). Next was sealing the chairs, but it doesn't look any different from the stain (because it's clear) so I though it would be useless to add a picture. REMINDER: do not stain any of the metal pieces or they will be sticky forever (which is why I mentioned the "proper" way to do this because all of that would be avoided but oh well).
So after some time and elbow grease, we now have this really nice patio set! All in all this whole project cost about $20. Happy refinishing!!