Every tweet ever created is an incrementing value, each tweet from the API is assigned id_str
This can be used as an offset for future requests
The value expected for max_id is the limit of the offset
So imagine the latest tweet result from the API the id_str is: 345923546427568120
Subtrack your tweets per page e.g 10 from that number and then do your next request with:
since_id=345923546427568100&max_id=345923546427568110 back 10 tweets
since_id=345923546427568090&max_id=345923546427568100 back 20 tweets
since_id=345923546427568080&max_id=345923546427568090 back 30 tweets
The initial 345923546427568120 value can be set somewhere e.g session or a js var to go forward after going back some tweets, or better yet cache the result set for a short time.
Hope it helps