The boy I have now, unfortunately, isn't really into much more than the occasional hand job. I have lived with several other male dogs who had different ways of asking for sex.
My first "my" dog was a Corgi and I pretty much had to get down on his level to do anything. When he was horny, he would sit in front of me and rock side to side, making soft little "grr, grr, grr" sounds. When I finally got on the floor with him, he would sidle up near my face and raise a hind leg to offer me access to his sheath.
Another was a Cattle Dog mix. He would get very, very affectionate and after a little petting and scritching, he would hook my arm with a paw and pull it towards his sheath. I would feel him up a little and then get on all fours and head butt him between his front legs. That was his signal to mount me over the head for a suck. He would get it in my mouth on the first try without any guidance from me.
At the same time I had another cattle dog mix who was neutered as a pup and he had a pencil dick. He was still quite horny, though! He would place a paw or rest his chin on my knee and give me this longing look. Very polite, unless he decided I was taking too long to get down to business. Then he would grab my leg and start rubbing his sheath on me fast and furious. Once I gave in, he would face fuck me like there was no tomorrow, knot and all. When he was hard, that pencil dick got way bigger and stayed that way for 10 minutes or so. Of course, if I did one boy, I had to do the other. They weren't too fussy about what order, as long as they both got theirs.
Later on, I had a Border Collie / Aussie mix who had the nicest cock on him of any dog I'd ever lived with and he enjoyed sharing it with me. He would sit and stare at me if I was doing something. If I wasn't paying attention, he would sort of sigh until I looked at him. Then I would go through his want list: "Do you need to go out?" No. "Are you hungry?" No. "Do you want to go for a walk?" No. And so on, until I got to, "Would you like to have your knot polished?" It only took him a couple of weeks to learn what that meant! If that was it, he would bounce and spin until I either got down on the floor with him or invited him on the bed.
All my boys had a signal that meant that I wanted sex with them. I would snap my fingers close to their flank, near the sheath. They would either start climbing on me or whatever they did to agree, or ignore it (or glare at me) if they weren't interested.