When it comes to Pest Snail removal and eradication, you really have three options: Physical, Chemical, and Biological.

Physical:
You set up a bait trap, with pieces of Zucchini, Cucumber, or lettuce. You wait till it has some snails in it, then lift up trap and kill contents, smashing and scalding hot water work well.
In addition, use a wide hosed gravel vacuum to suck them out of tank, or a turkey baster.

Chemical:
Copper Sulfate: This will eradicate all invertebrates in the tank and make it unsuitable for any inverts for a long time.

toddnbecka, “The copper sulfate won't bother plants or fish, but will kill any shrimp or other small inverts in the tank, and the copper ions absorbed by the silicone will then slowly leach back out for months, making the tank unsuitable for inverts long-term.”

Biological:
The snails are breeding out of control for a reason. 1, there is a lot of food in the water column; because you feed your fish too much; And 2, There are no natural predators in the environment.

If you have a small 10-30 gallon tank, the two part attack of introducing a predator and cutting back on feedings, will have a tremendous impact on the population of snails in your tank. For smaller tanks, Assassin Snails have proven effective. For larger tanks, some baby Clown Loaches will eliminate the population. (Research tank requirements of a Clown Loach prior to purchase)

Testimonials:
To loach or not to loach
http://www.aquaticcommunity.com/aqua...ad.php?t=82889
Kill snails while leaving cherry shrimp?
http://www.aquaticcommunity.com/aqua...ht=pest+snails
I might have a problem...
http://www.aquaticcommunity.com/aqua...ht=pest+snails
Overpopullating
http://www.aquaticcommunity.com/aqua...ht=pest+snails
Snail Math
http://www.aquaticcommunity.com/aqua...ht=pest+snails
Snails! Really?
http://www.aquaticcommunity.com/aqua...ht=pest+snails
Opinion on snail population management
http://www.aquaticcommunity.com/aqua...ht=pest+snails
Assassin Snails are my new best friend!
http://www.aquaticcommunity.com/aqua...ht=pest+snails
snail infestation? help!
http://www.aquaticcommunity.com/aqua...ht=pest+snails
Looking for a small snail eater
http://www.aquaticcommunity.com/aqua...ht=pest+snails
Invertebrates & Rid A Snail?
http://www.aquaticcommunity.com/aqua...ht=pest+snails
What species is a "pest" snail?
http://www.aquaticcommunity.com/aqua...ht=pest+snails
Snail Outbreak
http://www.aquaticcommunity.com/aqua...ht=pest+snails

In addition to these few testaments, there are countless more. Please fell free to share your testaments about Snail Control Below: