Personally, I would 'clay' the car first, before washing it (unless it's filthy!) - the idea is that it picks all the dirt up off the paintwork, and then you wash it to get rid of any residue. Need to be careful claying a car though, need to keep the clay warm and keep rotating it and folding it in to avoid scratching the paintwork. Also, use plenty of warm water - I tend to fill a bucket up with warm water, then add some car wash liquid - so don't put the car wash liquid in first, you don't want any bubbles! This provides lubrication for the clay, helping it to glide over the surface, picking up the dirt as it goes. Try youtube for an insturctional video.
Similarly, I would only polish by hand if you have not polished before - using a rotary polisher can easily burn or flatten the paintwork if you're not careful!
Then once you have clayed, washed and polished the car you can apply the wax. Again, you can smear it on by hand if you like, rubbing it into the paintwork, and then buff with a soft microfibre cloth.
Have fun!