See here for Youtube videos that may help you.
Green phone
Get Zitzaki!
Western phone: Steal the marked car. Drive to Zitzaki's old lab and use the horn. When he's in, drive to the J-Lab. After this probably most easy mission in the whole game feel free to go around the building until you get the rocket launcher.
Bank Robbery!
Eastern phone: Follow the marker to the Shark. Now drive it to the bank. Go to the entrance and kill the guards. Now follow the marker to the respray. After the respray, drive home as normal.
Yellow phone
Happy Gas Smash!
Western phone: Before you start this, Looneys should be neutral (but it isn't necessary). Go to the city university. Ring the horn on the marked spot. Instead of getting noodles, you'll be attacked. Kill the attackers. Now comes a rather annoying part. You'll have to drive around until you find an ice cream van and steal it. This can take some time or go fast. Usually around the church are some, but it may take some patience. When you got one, rig it at the nearby shop. Now drive to the Looney Asylum (Looney HQ). Park the van at the gas station and activate the bomb. Get out of there fast. When the station explodes, the mission is over.
Get Gama Rei!
Eastern phone: Kill a few people and wait until the medicar comes. Steal it. Drive to the marked hospital and wait for Gama Rei to enter the medicar. If only one cop hunts you, wait until he loses interest. Now drive Gama Rei into the marked garage. You should be fast enough so the Loonies don't catch you. If they do, just kill them (and maybe cops if you're hunted).
Follow That Traitor!
Third mission: Slowly follow the traitor and make sure he doesn't see you. Stay around one screen away from him. After you found the hideout, talk to Refried Noodle. Don't drive over him! Take him to the hideout. Three guys with Uzis wait there so come with a car and drive over them. When they're dead, the mission is done.
Red phone
SWAT Van Swipe!
First mission: Just get a wanted level of 4 (destroy cars and kill cops). The easy way is to do this before accepting the job (get rid of the cops by respray or car crush afterwards). When you have the SWAT Van, drive it to the garage near the red phone.
Stop the Tank!
Second mission: See the Youtube video to know where exactly to go. It's to the north. Make sure to have a fast car you can handle. If necessary, take the rocket launcher at the start of the mission. Take the rocket launcher and drive to the street with the tank. Run over the guys. Get out of the car and shoot rockets at the tank until it explodes. It should take four shots. There is a short time limit so make no mistakes.