There are a few basic ways to do play as engineer:
1. Play with the Pistol - Set up a Sentry to protect your team or intelligence, then charge with your pistol and shotgun.
2. Play with the Pistol and Gunslinger - Get into the battle before placing a Sentry, once someone shows up, place a sentry and start attacking them with your Pistol and Shotgun.
Using the Pistol is best if you want to venture forth, however, it does less damage than a sentry even when not being used by a Wrangler.
The Pistol is the secondary weapon for the Scout and Engineer classes. Its accuracy, while not exceptional, is superior to that of the Scattergun or Shotgun. It is useful for hitting targets at medium or long range or as a last ditch effort when the primary weapon is out of ammunition. The Pistol is very useful for destroying sticky bombs and taking out unsupervised sentry guns from outside of their range. The pistol suffers from medium damage falloff, despite being a single-projectile weapon, and combined with its relatively weak damage per hit, is often neglected by many players. However, when fired at maximum speed, this weapon is formidable in the hands of an experienced player, and has an extremely fast reload speed. In combination with the First Blood buff, the pistol is an incredibly lethal tool that can kill any enemy, overhealed or otherwise, in a single magazine. Like the Revolver and SMG, the Pistol fires a single, perfectly-accurate shot before 'bullet-spread' goes into effect, so long as the player has waited at least 1.25 seconds since firing the last shot.
3. Play with the Wrangler - Set up a Sentry (hopefully in a big enough area to warrant the Wrangler) and a Dispenser (to heal, fill up Sentry ammo and health) and stay there attacking everything and anything using the wrangler.
4. Play with the Wrangler and Gunslinger - Get into the battle and once comfortable set up your Sentry and possibly your Dispenser, and just go crazy with your Sentry using the Wrangler.
Note that the Sentry Gun Stats are just stats for the Sentry, the Wrangler will double the rate of fire.
Using the Wrangler, you are using the Sentry Gun as a weapon instead of the pistol. The Level 3 Sentry Gun is obviously more powerful than the Pistol, but you have to stay with it and the moment that you need to change to your wrench to fill up the ammo and health, you are defenseless for a few seconds while the Wrangler wears off.
The Wrangler also gives the Sentry Gun a shield that absorbs 66% of incoming damage, doubles the gun's firing rate, and increases the missile launch rate at level 3.
You may use the sentry missiles to Rocket Jump, this ability is particularly useful for reaching hard to get places.  (Also note that you can use the normal gunfire to launch yourself upwards, but you probably won't get too far without dying )