Ich habe Philosophie studiert!
I have philosophy studied/I studied philosophy! (remember the word order)
studieren belongs to the easiest kind of participles. If the infinite form ends in -ieren (fotografieren ..), the participle
ends in -iert and that is all we have to change.
Regular participles instead are constructed with the prefix ge- which becomes an infix if you already have a separable prefix:
aufstehen - aufgestanden, and ends with -t. Regular verbs are, for example machen - gemacht, spielen - gespielt and, important for
philosophers: setzen - gesetzt. To Verbs with inseparable prefixes, like vermitteln, we do not attach the ge-, so it may sometimes be difficult recognising
these participles.
Irregular (someone distinguishes a third group, but this is of no use to us) begin with ge- and usually end in -en. Examples: essen - gegessen. liegen - gelegen, but: bringen - gebracht. Well, these participles you will have to learn them by heart, at least the most important ones.
Alternatively, in every reasonable dictionary you will find a table of these verbs at the end. There is no other way of getting, for example,
from gestritten to the infinite form, streiten.