A bit of a vague question (like asking how the barbarians fought) as different cultures fought in different ways.

I haven't read any Indian history books lately but basically, north of the Deccan plateau (Aryans) were more cavalry oriented than the rest of India. Not too sure about the Pandyas and other southern peoples but the Oriyyas, Biharis, Bengalis, Assami and Arakanese made more heavy use of war elephants (also people in Ceylon). The Tibetans and later the Nepalis had superior cavalry and this was one of the reasons their influence was to great in the area.
The biggest difference between Indian armies and other European and Asian militaries was their size. There is a quote which sums it up really well (can't remember the exact wording, but its something like:
Persians were known for their archery, (someone) were known for their (something) and India was known for her armies.