How do you form a present participle to say eg: "I saw her sitting there" etc?

I saw her sitting there. : Onu orada otururken gördüm.

So you just suffix aorist with -ken / -kan?

Wow that was less complicated than I thought

Isn't 'saw' a past tense?

Wouldn't 'I see her sitting there' be a present tense?

Please correct me if I'm wrong, but aren't -yor or -yorum the present participles?

Onu izliyorum, geziyorum etc.

I'm not good at turkish but i think i can answer some of ur questions as far as english is concerned

*Isn't 'saw' a past tense?
yes it is, that's why the gördüm form was used

*Wouldn't 'I see her sitting there' be a present tense?
yes, then u'd use görüyorum ınstead of gördüm

*Please correct me if I'm wrong, but aren't -yor or -yorum the present participles?
they are not participles like english "sitting" but full verb forms conjugated in present tense. I'm not 100% sure, but i think turkish present participle are formed with -an/en i.e. oturan

in english "I saw her sitting" - "saw" is a verb form and "sitting" is a present participle. it is sometimes confusing as english tenses are constructed by means of participles, so it's necessary to distinguish whether the
"-ing" form is a participle, gerund or part of the verb. just compare:

she was SITTING - participle combined with past tense form of the verb "be" to form past continuous tense

SITTING here is prohibited - gerund (-ing form functioning as the subject of a sentence)

I saw a girl SITTING in the corner - present participle replacing an adjectival clause "who was sitting"

i forgot to add that turkish "otururken" could be analysed as OTUR (base form) + UR (tense suffux) + KEN (while)
thus otururken would literally mean "while she is/was sitting"