The dust in the interstellar medium is not like the dust you might find in your house. Firstly, the size of the dust grains is much smaller — they are typically less than 0.1 in diameter (more than a hundred times smaller than the width of a human hair)! Secondly, it is much less dense. With only one particle per cubic centimeter, collisions between dust particles are very rare. Understanding exactly how dust grains eventually come together to condense into planets and stars is an ongoing area of active research.
Dust is found throughout molecular clouds and can be seen in beautiful images of star forming regions like the Orion Nebula. Typically, there is about one hundred times more gas in these molecular clouds than there is dust. However, the dust is crucial the formation of these clouds. In order to form a hydrogen molecule, two individual hydrogen atoms must pass sufficiently close together to form a bond. In the very low-density ISM, such close interactions are rare. However, dust grains, while tiny, are still much, much larger than individual atoms — so interactions in which a hydrogen atom condenses onto a dust grain are far more common. When two hydrogen atoms condense onto the same dust grain, they can move around the surface until they find each other, and then are able to bond together to form a molecule, which detaches from the dust grain and goes on its way. Without the presence of the dust grains to act as a catalyst, the conversion of hydrogen from an atomic state to a molecular state would occur much too slowly to match the observations we see of the ISM.
Many dust grains have similar compositions to comets and asteroids. They may be composed of silicates, carbon grains, or water ice. Carbon monoxide is an important tracer of dust density, although in the densest, coldest dust clouds it may freeze onto dust grains and become undetectable.