Obtain permission from the person you are about to research. In most states searching for a person's arrest records is illegal without his permission. You generally will need a signed statement from that person stating that they will allow you to do this check on you.
Obtain information on the person you are researching. This information should include at least the person's full name, age and race. You can also narrow down your search by using noticeable tattoos or scars as well as their corrections number (if they admit to being arrested in the past).
Go onto your state's corrections website and locate the link to their arrest record and offender tracking page. This page will have you read through a few statements, and you will have to agree to the terms and limitations of the state. Once you do this you can enter the information that you have on the person into the different fields and perform the search.
Read through the information and the search results. It should give you a list of any and all charges that were held against this person. However, if the person is simply accused but never charged, or if they have been charged but never sentenced, the records may not be listed.
Call your state's corrections agency if you are doing a search on yourself and notice that there is any incorrect information on the list. The agency should be able to remove it, after a review.