The Spanish is consistent: use the infinitive. It's the English that's inconsistent: we sometimes translate it as the infinitive and sometimes as the -ing form. (We -- native English speakers -- know this naturally; English learners must memorize and it's very difficult because there really is no pattern or logic.)
To quote from the link below: To use one of the verbs from the previous list in a Spanish sentence, the first verb is conjugated, and the verb after the preposition is in the infinitive form regardless of how the English equivalent is stated. In English, the second verb will often be in its infinitive form, just like Spanish. However, sometimes in English, the second verb is in its gerund form: “–ing.”
btw, in English, "drinking" can be past, present, or future, depending on what surrounds it. Also, it can be a gerund (verb form used as a noun).
Isn't there a difference in meaning between "My friends stopped drinking" and "my friends stopped to drink". The first sentence would imply that your friends were drinking and now stopped it, the second sentence means that your friends stopped doing whatever they were doing to drink something.
The original Spanish sentence carries the meaning that they were drinking and stopped it.
Finish or end are basically synonymous (the same) and mean to complete something all the way.
John finished the race. (John ran the entire race)
The parade ended. (the parade completed its route)
I finished cleaning. (the house is now clean)
Stop is used when a task is quit midway, and is not completed.
John stopped running the race. (John could not complete the race)
The parade stopped (sometime went wrong, and the parade is stationary and not moving)
I stopped cleaning (my house isn't clean, but I am no longer cleaning it).
It is not when de comes before a word, but it is the difference between "dejar" (to allow) and "dejar de" (to stop). The additional word makes the meaning of the verb different. This happens in English, too. For example, you can throw some peas, or you can throw up some peas.
I don't know. I'd much rather throw a baseball with some friends than puke my guts out. They seem pretty different to me :) But yeah, I see your point. Both are an act of ejecting something away from yourself.
I think of "dejar" as opening my hands, raising them in kind of an "I surrender" fashion, and stepping back a pace or two. You're letting something happen, getting un-involved. In addition to "allow" or "permit", dejar also means "to leave" as in "dejé los papeles en la mesa" (I left the papers on the table). Again, open hands, raised, stepping back. You're getting un-involved with the papers.
I think of "dejar de" in the same way, but this time I'm backing away from the beverage. I'm "letting it alone", or quitting it. Becoming un-involved with it.
Dejar de doesn't mean to stop as in to put on the brakes or make someone else cease doing something. It means to refrain from doing it.
I really like the comment above about "let" being in the sense of releasing, becoming uninvolved open hands. It's really more a sense of leaving than "let" in the sense I usually use it. Very excellent, and I actually wonder if "let" should be removed from the drop-down definitions! Seems like other than "Let it go" there wouldn't be a lot of places you would actually use dejar in place of let.
dejar has several meanings depending on the context. See: http://spanish.about.com/od/usingparticularverbs/a/dejar.htm
In Spanish, we consistently use the infinitive in these situations; it's the English that can go with either the infinitive or the -ing form. -iendo or -ando is kind of equivalent to -ing in English, but that doesn't mean it's always used in the same way, so be careful.