This is an interesting question. Let's start by defining some terms to help us think about this problem! A solution is a chemical mixture that is comprised of a solute and a solvent. A solute is a substance that can be dissolved or dissociated in a solution, and a solvent is a substance that does the dissolving. I realize this is kind of abstract, so maybe we can use an example. Table salt is mostly sodium chloride, which chemically is written as "NaCl" (Na = sodium and Cl = chlorine). In its solid form, sodium atoms partially transfer some of their negative charge to chlorine atoms, which results in an "ionic bond." When you put sodium chloride in water, the Na and the Cl will dissociate, meaning they will separate into distinct ions Na+ and Cl-, and individually become surrounded by water molecules. Thus, in this picture, NaCl is the solute, which is getting dissolved in water, which is the solvent.

So now that we've defined these terms, let's think about your question: how do crystals form in water? Crystals can form from a solution when the solution is completely saturated and there is an excess of solutes. What does that mean? Let's look at our example of NaCl again. There is an extent to which NaCl will dissociate and be surrounded by water molecules. After a certain point, the solution becomes saturated. That means the solvent can't dissolve any solutes anymore. What results is the formation of crystals at the bottom of the solution.

As for your other question about what we do in my research group: I am working on a computer algorithm that will hopefully accelerate the discovery of a certain class of materials called block copolymers. Block copolymers are used in all kinds of applications. They are used in everything from household products, to tough or rubbery materials, to more advanced uses like drug delivery (getting medicine to particular parts of the body), and even possibly nanolithography (making computer chips) in the future!

Crystals grow when solutes (molecules dissolved in water) come out of the solution into regular structures. An example of this would be sugar in water. You can mix a lot more sugar into hot water than cold water. If you mix lots of sugar into hot water and let it cool, the sugar will slowly start to crystallize as it comes out of the solution. You can actually use this to make rock candy. Here's a recipe:
candy recipe

I do computational biology research in my lab. This means that much of my work is on a computer and I don't actually run any experiments in the normal sense. When you picture a lab (like on CSI) mine is very different. I have a desk and a good computer, but no lab coat or chemicals. I work to figure out the math that drives biological processes. Literally everything is a result of the math behind it, and my work is to figure out how biology works using math.