I find a very direct (but not confrontational) approach of asking for what you want works really well.
Just decide the tasks you want DH to do and say "would you please do x and y". When there's lots of stuff to be done, say "If I do x, would you do y? Would you mind doing it today?". Or "would you do y? I don't mean now, but if you could do it before tomorrow, that would really help".
You have to get over the fact that you have to ask him to do things. I know we think men should just notice and think of things to do, but they don't. You have to accept that and not resent it. So work out what it is you want to get done round the house and ask specifically. It really works! No hinting, or emotion behind it, just a straight request using "would you"... honestly, try it! If he says no, you just say "OK. I haven't got time to do it as I'm doing x, y, and z, so it won't get done before the weekend" etc then leave it. So he knows you're busy too.
Additionally (and this takes some getting used to), men respond really well to praise (think dog training). So when he does what you ask (even if he didn't do 12 other things you asked) say "thank you so much, I really appreciate it". When he regularly starts doing nice things say "you're so kind and thoughtful". Just like kids, anyone who is told they are one thing (clever, kind etc) becomes more like that thing. I'm not saying men are like kids or they are simple or anything, this kind of psychology works on everyone (managers do well to use it on their staff).
I've been doing it on my DH for a while now and it's great. I get him to do his share of the work and we're both happy. For example, I said to him yesterday "We're running low on food (he never notices this). Would you have time at the weekend to go shopping?" He suggested one of us go to the market/local shops and the other can go to the supermarket. He offered to take our DD with him. Problem solved and I don't feel like I have to do ALL the shopping again.