Wax and Polish are two different things. Polish is there mainly to get the "top layer" of crap off your paintwork and reveal and fresh layer underneath. However, to seal in this shine for longer, you then need to apply wax after. One thing to note down though, you need to clay bar a car FIRST before applying polish or wax, as the grit stuck to the paint will be rubbed in.

To get the ultimate shine, you should really look into getting a claybar on the car and then using a rotary to correct any swirls the paintwork will have, as swirls are the exact thing that rob a paintjob of it's shine.

If your only wanting to do it by hand though, then I would do it like so...

Give the car a good rinse, then a wash. Use the two bucket method (One with clean clear water, and the other with your shampoo in). When washing the car, always do the wheels and arches first and then do the body top to bottom. Only use MITTS (Lambswool preferably. You can find budget ones in Halfords.) and DO NOT use sponges.

Once the car has been washed and rinsed, proceed to clay bar the car. Don't bother drying the car after washing as you need to keep the paintwork nice and lubricated, so the water will help with this, as well as the spray that comes with the clay bar kits. The clay bar helps pick up all the grit to stop you from rubbing this grit into the paint when waxing or polishing. A car only needs to be clay barred every month I would say.

Then re-wash/rinse/dry the car. Only dry the car with the proper drying towels or a blower if you have one. DO NOT use one of those squeegee things I see the "£2 car wash" people use.

At this point, you need to polish the car. Quite simple, apply between 1-2 coats and let it cure a little, then buff off with a microfiber cloth.

You could re-wash/rinse/dry the car again, but if there's not much polish dust, then you could probably get away with blowing off any polish dust with a blower.

Now you wax the car. Apply as many coats as you like. The more you apply, the more protection your car gets and the easier it will be to clean next time. 3-4 coats should be sufficient, and you can also use wax on the wheels. A little tip for you, apply the wax with a clean, damp microfiber cloth. The dampness of the cloth will help you in applying the wax.

If you have the spare cash, you should also invest in some finishing detail spray.

And just to note, PLEASE PLEASE PLEASE use the correct cloths, and not ones that are old clothes or random cloths riddled with tags. This will only do your paintwork more damage than good.