The first thing you want to do, is to head down to your local costume shop and check out all the costumes which they have. You should jump right in and look for a Luigi one, because if they have it, then you are good to go right away.
However, if they don't try and look for a Mario one, which you can edit later. Now if they have a Mario one, all you need to do is replace the red shirt on the inside with a green one and then replace the 'M' on the hat with an 'L'
Now if they don't have either, you are going to have to get the costume built from the ground up, which shouldn't be too much of a problem.
Now go out and buy some overalls. Make sure that they are blue, since you want denim overalls, which match the ones that Luigi wears. After you have gotten the overalls, get a full sleeved green shirt. This is the shirt you will be wearing on the inside, so you need to make sure you get the right one.
Now you need to get a pair of white gloves, make sure that you get plain ones, since you don't want to mess up your costume. Now get a hat that looks like Luigi's hat, or get a cap that is of the same colour. Go on and create a big 'L' on it.
The last thing which you need to pull off the look is a pair of brown boots or shoes. Remember to get rounded shoes, since that is what Luigi wears.
Once you have everything, just wear it accordingly and then go on and head out to the costume party.