There isn't really a "correct" way to go about doing things when it comes to having sex. You can certainly try new things if you want to. If you want to try that position in particular, the man is behind, the woman is in front. Not sure how else to explain it without being too sexually explicit. If you want to try it, go for it. It isn't too difficult to figure out once you're actually trying it.

so long as you insert it in the appropriate hole, i think you're fine!

assuming that you're referring to the vagina, is it still possible to do it with the doggy style as the vagina is in front...

Yes, doggy style still refers to putting the penis in the vagina. Doggy style is not the same as anal sex.

If your partner is in the position for doggy style (her on her hands and knees, with her head up or perhaps on a pillow) then the anus and vagina are more in a "stacked" position, with the anus on top and the vagina on the bottom, like book shelves.

To make it easier (till you get the hang of it) I would get on all fours first, lean down on my elbows, arch my back (raising my rear end up) so that the angle is right, and let him enter you from behind. Don't move much at first to make sure that he isn't going to slip out or something.

If that seems a little too risque, you could always try it laying side by side in the spooning position with him behind you. That one's pretty easy to do, and nice too because you can still cuddle.

There is no correct way, but my favorite way is lying down with apillow under my stomach to help raise the end a bit. Have fun!

It might be more natural to you if you start in the spooning position (easier with your top leg up, on top of his) and kind've roll over so you are facing the bed and he is on top, then work your way up so you are on your knees.

It's one of my favorites.

One has to be an expert in yoga to do this. The man has to stand on his head, leg high up and straight. The woman has to clutch her hands to a hook hanging down from the ceiling. It is then possible to do get it right. A hugely flexible body and some practice, you can do it exactly Doggy style

???
No, not right.

Nothing about the doggy position explicitly indicates which orifice is being used. It's simply a position that two bodies are in during intercourse