When do you use the words "ab" and "an?"
I've noticed these two words being used in certain sentences like, "Bieg nach links ab," and, "Sie ruft ihn an." These sentences translate to, "turn left," and, "she calls him." I can see how the word "nach" implies direction, and the words "bieg" and "links" imply turn, and left, and in the second sentence, the words "sie" "ruft" and "ihn" translate to "she" "call" and "him," respectively, but I can't find what the purpose is for the words "ab" and "an." I'd like to know when you're supposed to use these terms, and what they convey.
In these cases, the prepositions "ab" and "an" are part of the verbs. These are so-called "separable verbs" (trennbare Verben). An explanation on canoo.net: http://www.canoo.net/services/OnlineGrammar/InflectionRules/FRegeln-V/Texte/Trennbare-0n.html?lang=en
The first verb, infinitive, is "abbiegen".
You can form sentences with this verb like:
Sie können hier abbiegen. (You can turn here.)
Sie biegt nach links ab. (She turns to the left.)
Only the two parts of the verb together -- "ab" and "biegen" -- define its meaning. There is a verb "biegen", too. But this means "to bend". (For example, bend a piece of metal.)
Whenever you see a "lost preposition at the end of a German sentence", you should check whether this is a part of the verb.
The same applies to the verb "anrufen":
Sie können anrufen. (They can call.)
Sie rufen heute an. (They call today.)