Both of the molecules are used to store and regulate the use of genetic information in a living organism. They are both built using essentially the same molecular structure, being phosphate groups and sugars chained together as a "backbone" with variable nitrogenous bases utilized as the "alphabet" by which the information is encoded.
The sugar used in RNA is ribose, as opposed to deoxyribose in DNA. The difference is the absence of a single oxygen atom in deoxyribose. DNA is normally double-stranded whereas RNA is normally single-stranded, although it possible and observed for RNA to be double-stranded as well. RNA can make use of a number of additional nitrogenous bases that aren't found in DNA, such as pseudouridine and dihydrouridine. RNA can also take on relatively unique shapes, such as the tRNA form, which are critical to their function. RNA also uses uracil instead of the thymine found in DNA. DNA is used for long-term, highly-conserved genetic information, whereas RNA tends to be shorter-term, production-based disposable copies.