Having seen your last question about the translation of 'da tanto tempo', I can see why you are confused about these expressions.
Basically, the Italian word 'da' can be translated into English in two ways:
'For' followed by a PERIOD of time.
'Since' followed by a POINT in time.
So, for example, you can say:
For a long time
For ten years
For five minutes and so on
or
Since 3 o'clock
Since November
Since 2005
Here are some examples with your original sentence:
Non vado a pescare da tanto tempo = I haven't been fishing for a long time
Non vado a pescare da sei mesi = I haven't been fishing for six months
Non vado a pescare da molti anni = I haven't been fishing for many years
but
Non vado a pescare da settembre = I haven't been fishing since September
Non vado a pescare da 2012 = I haven't been fishing since 2012
Non vado a pescare da quando ero bambino = I haven't been fishing since I was a child.
I hope that helps. Please ask again if anything's not clear.