I took my chainrings off for cleaning and now I don't know how to put them back with the proper orientation. Which way faces out?

Also, am I supposed to but both rings on the outside of the spider? Both on the inside? One on each side?

I'm certainly not an expert as my bike has only one chainring but recently I installed a new larger one. Try looking closely for any indentations so the ring will seat securely into the crank, thats what worked for me.

What kind of rings are they, how many?
With Shimano chainrings the tooth count stamping on the big ring faces out, to the right. All other rings face left, toward the frame. They are bolted on either side of the spider.

Al

If you have a shimano ring, the shimano tech docs site will have specific instructions on how to mount the c-ring properly for optimal shifting.

If it's the big ring then it's usually a small anti-chain jam pin that is orientated to be right next to the crank. Smaller ring is the little bump in the inner diameter of the chainring. This is all explained in the tech docs clearly.

Next time when u open a patient's chest, make sure ur able to put everything back together, and not leave any tools inside.

Most chainrings have countersunk holes for the mounting bolts. The countersink depressions face away from the spider, i.e., outward on the outer ring and inward on the one (or two) inner ring(s).

Put it so the writing is out if it's the bike one. Similarly on the middle ring. Any stampings should face out.

Also if there are any shifting aid pins the larger part should face inwards on the big and middle rings. Do not confuse this with the anti jam pin on the big ring mentioned above.

On the chainring bolt holes if there is a step then the step should face to the outside on the big ring and the inside on the middle ring.

If it's the small ring they usually don't have a shoulder or shift aids to either way is fine.