The present active participle is formed with the suffix -щ- (plus adjective endings). It is based on the present (i.e. non-past) stem of the verb, so that if you replace the -щ- with -т- you'll get the 3rd person plural form of the verb e.g. писђть/пќшут: пќшущий, говорќть/говорїт: говорїщий.
Like all long-form participles, they are characteristic of written style and can be paraphrased with a который-clause in conversational style:
Ћн рисџет детљй, игрђющих во дворљ. He is sketching the children [who are] playing in the courtyard.
котћрые игрђют во дворљ. (Same meaning.)
Like other participles, the present active participle often occurs in box constructions. In the following version of the above example, the words во дворљ are boxed in by the Accusative Plural forms игрђющих... детљй (Lit. 'the playing in the courtyard children'):
Ћн рисџет игрђющих во дворљ детљй. (Same meaning.)
Note that the word present in the grammatical term present active participle refers not to the meaning of this form, but to the fact that it is derived from the present (i.e. non-past) stem of the verb.
The meaning of this participle is: action performed simultaneously with the main verb of the sentence. Thus, if the main verb of the sentence is past, then the participle will also refer to past time:
Ћн рисовђл детљй, игрђющих во дворљ. He was sketching the children [who were] playing in the courtyard.
котћрые игрђли во дворљ. (Same meaning.)
Participles derived from verbs ending in -ся never have the variant -сь.
занимђться/занимђются: занимђющийся, занимђющаяся, занимђющиеся...