Replacement windows are a huge business. There are a couple different types. Replacement windows are made specifically for your existing openings. Your old sash get removed and replaced. In most cases, no additional work is needed for interior and exterior trim, it doesn't get touched. The most common replacement windows are for double hung style windows. You didn't say what type of windows you have.
The most common and inexpensive replacements are vinyl. Normally, there are local companies that make these type of replacements. They'll come out and measure your existing windows. Larger window manufacturers also make replacement windows and you can get wood sash if you prefer and in numerous "looks". Companies like Anderson, Marvin, etc. offer replacements, custom made for your house.
Completely replacing your windows will involve a lot of work since interior and exterior trim, along with the entire window and frame get taken out. This is the most expensive and time consuming way to go. New windows may not fit the exiting framing and you are often looking at a complete house paint job, in and out.