Present participle: ringing
Past participle: rung
The verb to ring is an irregular verb, which means that you have to learn by heart its various forms, especially in the past tense. Past participle can be found in the table of irregular verbs, the third column - it is a part of the verb used to form tenses such as present perfect and past perfect (have rung and had rung).
On the other hand, present participle is easy to form - you just add the suffix -ing to the verb and that's it! So, ring + -ing = ringing