Let us assume your variable levels are A, B, C, and D. If you have a constant term in the regression, you need to use three dummy variables, otherwise, you need to have all four.
There are many mathematically equivalent ways you can implement the dummy variables. If you have a constant term in the regression, one way is to pick one of the levels as the "baseline" level and compare the other three to it. Let us say, for concreteness, that the baseline level is A. Then your first dummy variable takes on the value 1 whenever the level is B and 0 otherwise; the second takes on the value 1 whenever the level is C and 0 otherwise, and the third takes on the value 1 whenever the level is D and 0 otherwise. Because your constant term is equal to 1 all the time, the first dummy variable's estimated coefficient will be the estimate of the difference between level B and A, and similarly for the other dummy variables.
If you don't have a constant term, you can just use four dummy variables, constructed as in the previous example, just adding one for the A level.