I'm sorry, but "izahlı metotla" is totally incorrect...
I don't know how to say it on Turkish, but on English "методом тыка" means something like "by hit-and-miss method/fashion; by guesswork; by rule of thumb".
And moreover, here is used a play on words and that's the whole point of the phrase. Play on words is that this "методом тыка" is used both in its direct and figurative meaning.
Direct meaning: I'm treating sterility by means of proding/poking/sticking.
Figurative meaning: I'm treating sterility by hit-and-miss method/by guesswork/by rule of thumb.
In the Russian original these two meanings are implied in ONE sentence. So I dunno if it's possible to find some expression on Turkish which would have same two meanings in one...
I hope I could explain well what I mean
P.S.: IMHO I find this phrase/joke a bit indecent due to its direct meaning...