Aye! I use the Big H's own brand if I'm washing by hand, or Meguiars Hyper Wash if I'm going to use my Gilmour foam gun.
I'd say use a foam gun if you have one (or can borrow one) so you improve your chances of getting all the grit and rubbish off the surface before you attack it with clay and polish (saves recycling the grit all over your paintowrk).. Otherwise make yourself a solution of shampoo/water and spray it on the car using a pump/trigger bottle (old window cleaner, kitchen or bathroom spray bottles - rinsed - will do).
Hose the beast down to get it wet. You don't need to drown it.. just make it wet, leave it to "soak" and then squirt it again. Pay most attention to the sides, where most of the dried on dirt is going to be.
Once the dirt has turned to "mud", spray it with the shampoo/water mix and again leave it to soak in. This step will loosen the stuff on the surface and make it softer, in case it's still there when you wipe the surface during the wash proper.
Rinse all that soapy layer off... that should carry off most of the larger and softer material, though stubborn mud streaks and other dirt will still be there.
Now wash your car as normal... use the microfibre/wool mitten doodah instead of a sponge.. but sponge is okay if you double-bucket and rinse it frequently to get the dirt off it.
Hose it down, chammy it dry (people don't like chammy's but logically if you cleaned your car properly there should be no grit to stick into the chammy and cause swirling) or use a micro-fibre towel etc.
Then the beast is ready for a clay/polish etc. but this is a good point to have a cup of tea (so your missus thinks you're finished.. actually you only just started!