I have decided to get my mercury amalgam fillings removed because I do not trust the controversy surrounding them.What is the safest way to get them replaced with composites?Any info appreciated.
In reply to doctor matt there has been controversy and it is still going on http://en.wikipedia.org/wiki/Dental_amalgam_controversy
but I appreciate the info.
What precautions will the dentist take to prevent me from inhaling mercury vapour when he/she drills out my filling?

There is no safest way. They are just removed and the composite is put in. Much better choice than amalgams.

go to any dentist and they can remove the mercury fillings and replaced it with tooth colored restoration.no risk at all,but tooth colored restoration would be slightly more expensive then the mercury fillings.

There is no controversy surrounding them except that which is made by ill-informed or mischievous people. Regrettably some dentists are dishonest too, for the sake of making more money. If any dentist makes the statement that your health will be better if you have the amalgams removed, then he/she is making a health claim that is unjustifiable and would be wide open to legal prosecution.
If you decide to have composites instead for aesthetic reasons, then that would be more reasonable.
The placement technique is more exacting and time-consuming than amalgams and will therefore cost more.
Small composites can be placed directly in the cavity as long as the area is kept very dry (sometimes a rubber dam is used), and it is built up in small increments (each increment shrinks a little upon setting).
If it is going to be a very large filling, then it would be best if you chose composite or porcelain inlays that are made out of the mouth and cemented in, rather than direct composite buildups in the mouth. They will be stronger and better fitting this way.

Honestly the "mercury" fillings risk is so controversial, I wouldn't jump to have the amalgam ones removed. This could cause structural damage to the teeth. The exposure to Mercury is lower than eating tuna fish. You could go back to your dentist and request the change. But. unless there is a problem with them, your insurance will not cover it. I have both, and they are many many years old, why fix it if it isn't broke? Talk to your dentist and ask his views.

the good idea but it must be done by expert dentist.

The biggest problem with amalgam exposure is not when you have them already but when you place or remove them.There is controversy about amalgam fillings which lead to the situation that it is not used in Norway for example anymore and other Scandinavian countries are about to follow.In Germany,retrograde fillings after apicectomies are not allowed to be filled with amalgam since 20 years.There was research done indicating that amalgam compromises the immune system....In a study that I read some time ago over 70% of people of unclear illness symptoms felt better after amalgam removal.There is no direct proof for it,but I think it is also very difficult to proof the negative effect of amalgam.One user before said you get the same mercury exposure with amalgam as with tuna.That is statistically correct.Only that you have amalgam in you mouth every day for several years and I guess you don't eat tuna every day.So it is up to you.Amalgam is definetly a longlasting material,which you can have for 40 years if it is well placed,but white composite is of course more estehtic.Rubberdam placement and very good suction are essential during amalgam removal but I heard that there are not so many dentists in the states that like to perform these procedures...So good luck!