Assassinating Tamir with Style
Your first main target in Assassin's Creed is Tamir the Black Market Merchant. This is a really easy assassination. If you still need your "Blade in the Crowd" achievement just select your Hidden Blade, walk up behind him and press the X button (Square on PlayStation 3). If you've already done it that way and want to try a fancy pants assassination, then this guide is for you! Remember that this happens in Memory Block 2 so you won't have Throwing Knives or the Counter ability during the investigation.
PREPARATION
Before visiting the Assassin's Bureau you may want to familiarize yourself with the Al-Silaah Souk (market) and its central courtyard. Look for the grape arbor (lattice on four poles) over an octagonal pool as pictured below. A ladder leads up the arbor at one corner. It's easy to lose your sense of direction in the square courtyard. Just remember that the ladder is on the eastern corner of the arbor.
Now is a good time to practice Free-stepping through the Souk. The halls are so tall that there are upper and lower beams on which to Free-step. Once on the lower beams, it's difficult to make your way to the upper beams. Practice leaving the courtyard on the upper beams. There are two hallways leading from the western corner of the courtyard. These are the preferred exits because they are straight, end with a haystack, and are on the way back to the Assassin's Bureau.
After the Rafiq gives you the feather, just walk into the central courtyard of the Souk. Tamir will arrive once you move to the northeast end of the courtyard. I prefer to approach by ground. The Souk is bustling with foot traffic that you can push your way through. A rooftop approach is also possible but gains you no advantage. If you do choose the rooftop route and jump onto the arbor, realize that you aren't able to climb up or down ladders once it says "Ancestor's memory synchronized. Now recording." It may feel like you're stuck on top of the arbor. Don't panic - just drop over any edge and let go.
Position yourself near the ladder during the cutscene (i.e. the "scene" where Tamir "cuts" that guy.) 
HUNT
After the cutscene Tamir rounds the southern pole of the arbor, passes by the eastern pole (where you might be standing next to the ladder) and scolds the merchant at the northeast edge of the courtyard. He then proceeds in clockwise order around the courtyard and scolds three other merchants before starting over at the first one again. Refer to the map below for the location of the four merchants (green dots), Tamir's tour (in yellow) and recommended escape routes (in red).
You can hear Tamir from anywhere in the courtyard. Here's the gist of each rant:
- Merchant 1: "Pathetic!"
- Merchant 2: "Melt it down."
- Merchant 3: "You begged me for this position."
- Merchant 4: "Why can't you sell these things?"
There are several stationary guards and others that roam in and out of the courtyard. None are very observant except for Tamir himself. Don't let him see you jumping or hanging from anything. If you find yourself face to face with Tamir, hold the A button (X on PS3) to Blend until he passes by. There's a beggar who waits next to the second merchant. If you move anywhere to the southeast of the arbor, she will come out and bother you.
The real nuisance isn't the beggar or even the guards, it's all the Jar Carriers. They walk everywhere except through the bloody pool. Be careful to give them a Gentle Push by holding the B button (Circle on PS3).
In any event, Tamir never leaves the courtyard. If you become exposed he stands and fights. If he discovers a dead body he says, "This will be bad for business." Typical businessman.
ASSASSINATION
My favorite technique is called "air to assassinate". The first thing you need is a place to stand above the target but not too high. The arbor is an obvious choice. If you stand on top of the arbor it's just a little too high (UPDATE: My mistake. Air to assassinate is possible from on top of the arbor if you get a running start.) However, hanging off any corner is just right, with your feet tucked against the angle braces ready to push off.
Climb the ladder to the top of the arbor. Make sure your hidden blade is selected. The perfect time to strike is when Tamir is chewing out the third merchant. Move to the western corner and face this merchant. Don't hang over the edge yet! If Tamir sees you doing that you're busted. As Tamir approaches, target him by pulling Left Trigger (L1 on PS3). Then wait until Tamir turns his back to you and says, "You begged me..."
The easiest way to pull off the air to assassinate is to start with a Drop to Grasp. That's where you pull the Right Trigger (R1 on PS3) and run to an edge. Altaïr throws one arm up to catch his balance before Dropping and Grasping the edge where he was just standing. It's not the most graceful looking move in the world. As he drops, let go of the Left Thumbstick but continue to hold the Right Trigger. Then tap the X Button (Square on PS3) and the rest is automatic.
ESCAPE
This escape is almost as fun as the assassination itself. One advantage of assassinating Tamir while he talks to the third merchant is that it positions you in the western corner. Quickly climb up to the high wooden platform there and escape by Free-stepping across the upper beams until you emerge from the Souk by landing in a haystack. I prefer the hallway to the southwest but the one leading to the northwest works also. In fact, the northwest hallway has the advantage of being able to reach the haystack from even the lower beams, provided you stay to the left.