usage of 'auf'

Hi . 

'auf' is used as 'for' as in 'auf ein Taxi '. 
As well as 'on' as in 'auf dem Weg' . 

How do we know when to use it correctly in the sentence?
Thanks !

Hallo Vidya-manuS!

Prepositions like auf can be the trickiest type of vocabulary to learn when you're starting with a new language because they don't have set equivalents across languages - the way that one language's prepositions are used is not going to match up exactly with how another language's prepositions are used. Therefore, the easiest way to approach prepositions is to learn them in context. 

It looks like you've already learned at least two sentences where auf appears - something like Sie ist auf dem Weg zum Hotel "She is on the way to the hotel," and Warten Sie auch auf ein Taxi zum Zentrum? "Are you also waiting for a taxi to the city center?" Now that you've seen these, you can log away or make a note that you use auf when you want to say "on the way" (auf dem Weg) and when you want to say "to wait for" (warten auf). If you start to build a list for yourself of situations like these (particularly of which verbs prepositions are used with), you'll begin to learn when and where prepositions like auf should be used.

I know this isn't an easy answer - each preposition has so many uses that they can't all be neatly explained! - but I hope that it has still been helpful! Do let me know if you need any more clarification on this.

Tschüss!

Liss