Hint 11: Don't worry that you fall off the walls - in The Witcher you can't fall off anything that hasn't been designed this way.
Don't trouble yourself with archers (M1.11) who try to shoot you from below - you can't harm them for now. Just run past them.
After a cut-scene another bandit will attack you (M1.12). Another one (M1.13) will engage in a moment.
Hint 12: Remember to adjust your fighting style to the enemy you are fighting. Use the fast style to attack the fast ones, and the strong one to attack the strong ones. Simple as that. If you see that your blows don't do much to a certain type of enemy, just switch to the other style.
Run to the archer (M1.13) - try to do this as fast as possible. Defeat some more bandits (M1.14, M1.15). Notice the barrel laying against the wall (M1.19) - it's the first container in the game that you can loot.
Deal with three bandits by the gate (M1.16) - it's easiest to keep them standing on the stairs so you can take them one by one. Remember to switch your style - there are two slow enemies and a fast one. Use the turnstile to open the gate (M1.17).
After a cut-scene you will get two potions: a Thunderbolt and a Swallow. As told by Vesemir, use the former at once. Leave the Swallow for later - you might not need it in tutorial at all.
Hint 13: The Swallow (potion that helps you regenerate) is best held in a belt. This way you can access it during combat much easier.
When on your way to the entrance (M1.18) notice that there are some remains of the last archer you beat (M1.15) - loot them. Talk to Triss and other witchers to know more about potions, the Professor and Savolla. Click the gate (M1.18) or talk to Leo in order to get inside.