How to implement dummy variable using n-1 variables? If I have a variable with 4 levels, in theory I need to use 3 dummy variables.  In practice, how is this actually carried out?  Do I use 0-3, do I use 1-3 and leave the 4's blank?  Any suggestions?
NOTE: I'm going to be working in R.
UPDATE:  What would happen if I just use one column that uses 1-4 corresponding to A-D?  Will that work or introduce problems?
 A: 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.
A: In R, define the variable as a factor and it will implement it for you:
x <- as.factor(sample(LETTERS[1:4], 20, replace = TRUE))
y <- rnorm(20)
lm (y ~ x)

which returns
Call:
lm(formula = y ~ x)

Coefficients:
(Intercept)           xB           xC           xD  
     1.0236      -0.6462      -0.9466      -0.4234  

The documentation for 'lm', 'factor', and 'formula' in R fills in some of the details.
A: whuber told you in the comments that coding a 0-3 or 1-4 coding instead of creating dummy variables isn't what you want.  This is try - I am to hopefully explain what you would be doing with that model and why it is wrong.
If you do code a variable X such that if A then X=1, if B then X=2, if C then X=3, if D then X=4 then when you do the regression you'll only get one parameter.  Let's say it ended up be that the estimated parameter associated with X was 2.  This would tell you that the expected difference between the mean of B and the mean of A is 2.  It also tells you that the expected difference between the mean of C and the mean of B is 2. Some for D and C.  You would be forcing the differences in the means for these groups to follow this very strict pattern.  That one parameter tells you exactly how all of your group means relate to each other.
So if you did this kind of coding you would need to assume that not only did you get the ordering correct (because in this case if you expect an increase from A to B then you need to expect an increase from B to C and from C to D) but you also need to assume that that difference is the same!
If instead you do the dummy coding that has been suggested you're allowing each group to have its own mean - no restrictions.  This model is much more sensible and answers the questions you want.
A: In practice, one usually lets one's software of choice handle creating and manipulating the dummy variables.  There are several ways it might be handled; here are several common possibilities for a data set with four observations, one at each level of A, B, C, and D.  These are different parameterizations; they result in exactly the same model fit, but with different interpretations to the parameters.  One can easily convert from one to another using basic algebra; note they are all linear combinations of each other; in fact, any linear combination can be used.
Use differences from the first level (default in R):
A 0 0 0
B 1 0 0
C 0 1 0
D 0 0 1

Use differences from the last level (default in SAS):
A 1 0 0
B 0 1 0
C 0 0 1
D 0 0 0

Use "sum" contrasts:
A    1    0    0
B    0    1    0
C    0    0    1
D   -1   -1   -1

Use "helmert" contrasts:
A   -1   -1   -1
B    1   -1   -1
C    0    2   -1
D    0    0    3

