Learn Spanish (Latin America): Mi abuelo cose el cuero desde hace mucho tiempo. - My grandfather has been sewing the leather for a long time.

In Spanish, when an action started in the past and is still happening right now, you use the present tense. Because the grandfather is still sewing leather, we use the present tense cose along with desde hace to express "has been sewing".

How exactly does desde hace mean "for"?

Desde usually means "since" and hace is used to show passed time. When put together as desde hace before a length of time (like mucho tiempo), it translates to "for" to describe how long an ongoing action has been happening.

Could I use por instead of desde hace to say "for a long time"?

You can, but desde hace is the most natural choice here. Desde hace specifically emphasizes that the action started in the past and is still continuing today. Por just states a duration of time, and is more commonly used for actions that are completely finished in the past.

What verb does cose come from?

It comes from the verb coser, which means "to sew". It is a regular verb, so to match mi abuelo (he), we drop the -er ending and add -e, giving us cose.