Fetching details from the dictionary...

to fit (e.g. a pane into a frame); to insert (e.g. a cork); to fasten (a button)
to put on (something that envelops; e.g. a ring, gloves); to place (a hoop) around; to attach (e.g. a hose to a tap)
to pigeonhole (into a particular category); to force (into a mold); to place (restrictions) on
to entrap; to take (someone) in; to set (someone) up; to deceive
to throw into
to have sex; to fuck
部品をきちんとはめないと動かないよ。
It won't work if you don't fit the parts properly.
婚約記念の指輪を薬指にはめて鏡で確認した。
I put the ring on my finger and checked in the mirror.
指輪を薬指にはめると誓いの意味がある。
Putting a ring on the ring finger carries the meaning of a vow.