"He was talking and looking at his own dog."
Translation:Mluvil a díval se na vlastního psa.
Actually in this case I think our main translation is not the best there is. HIS OWN is better and also more commonly translated as SVÉHO VLASTNÍHO. Literally the same way English has it.I am not saying that nobody would not say just vlastního but I sure would not.
svého is just "his"
The clitic "se" needs to be in the second position of the clause. The first clause is "mluvil", then we have "a" connecting the clauses, and the second clause begins with "díval", followed by the second position where we put "se".
If we add a word to the first position, "se" will remain second and "díval" will move after that, for example: "Mluvil a přitom se díval na psa" - He was talking and looking at the dog at the same time. (Or: He was looking at the dog while he was talking."