This mission is actually the mission you may have seen in a whole bunch of promotional videos and they cover pretty much the entire mission. Again, this is still something of a training mission. You won't receive a whole lot of prompts but the difficulty will still be scaled back and be more forgiving.
Once you disembark from your APC, follow your squad to meet with Captain Cole. You'll find him in what looks like a Market area and meet around some pallets and a map. You'll find out what your mission is and then head off beyond him. Just follow along with your squad and you'll enter a building and move through it. As you go to exit the building, you'll see a patrol pass by but don't do anything, just wait for it to pass by. You'll cross a street and then enter another building, a garage. Once you get back outside, you'll be presented with another QTE. Finish that QTE and get back into the fight.
You'll have a giant parking lot filled with enemies, I recommend you take cover with your squad off to the left (as in the E3 demo if you've seen it). Clean up whatever enemies you can but stay in cover and be cautious. Wait until the white van gets destroyed by an RPG and then move up on the long right side towards his position. You'll actually be presented a marker with his location so just aim for that and shoot bursts until you take him out. Be careful because you'll get attacked by reinforcements coming from the far corner from where you entered the area. Just stay and defend and eventually they will exhaust themselves, then move back to the garage.
Instead of exiting the way you came, your squad will exit through the other door of the garage and climb up through the building and into a large, dark room. When you get close to the end of this room, a couple of enemies will enter the room and take cover behind a desk so be sure to find cover. Take them out and head through the door they came through. Make your way to the roof and wait for your squad to start moving across.
Just do what your squad does until they all go prone and crawl across the roof. Follow behind them and do as they do until they give you the rocket launcher. Take it and wait for them to give you supressing fire. Then pop out of cover aim for the orange marker. At this point, you'll be told to provide cover for the people picking up your downed squad mate. Look over the street below and look along it long ways. Most of the enemies will come out of and take cover on the left side of the street. Just watch for them and take them out as they pop up.
After you've cleared the streets below, you'll have to exit the roof. Follow your squad as they create a bridge to the next roof. Follow them down from the roof and make your way through the markets below to a large wooden door. You'll make your way through the big door and around a corner. You'll be attacked by enemies in the next hallway taking cover behind rugs. Be careful because there's also a side hallway about halfway up that enemies can come from and this is actually your destination.
Once you exit the building, take cover by the Humvee and the van. Wait until you "get elected" and look at the wire moving from the corner of the van to one of the nearby buildings. Follow the wire into the building, down some stairs and into a vent. You'll follow it through the vent; drop out of it and into a room in the basement. Pull the plug out and you'll be attacked by a bunch of QTEs. Complete them to finish disarming the bomb. After you've done so, just head back up the stairs until you get back outside. Return to your squad and they'll tell you to grab the LMG up on the overpass. Grab it and go prone. Just keep taking out enemies as they come, blowing up vehicles with the powerful weapon as necessary. Eventually you'll have to retreat and use a truck mounted machine gun. Take control of that and start shooting at the enemies on the side street. Keep clearing enemies until something really bad happens...

