Pick up a good electronic bass tuner. While a guitar tuner will often be sufficient, it's even better to buy a tuner that is designed to tune bass guitars, as it will be able to pick up on the very low sound of an unplugged bass guitar. Your local guitar and bass shop will have electronic bass tuners.
Turn on your electronic bass tuner and grab your bass. Hold the tuner right up to the bass' body, preferably a few inches away from the string. This will allow the tuner to register accurate notes and will aid in tuning your six-string correctly.
Pick the thickest bass string and look at the tuner. If your bass guitar tuner shows any note other than a B, then this string is out of tune. Tune up if the note that is displayed is either a A, E, F or G, and tune down if it's a D or C. Pay close attention to the tension, as this will also aid you in determining whether to tune down or up.
Hit the next string down and see what note is registered on the tuner. You want to see an E on the tuner, but if you don't, you'll need to tune up or down to get the string in tune. The musical note scale is A-A#-B-C-C#-D-D#-E-F-G-G#, in ascending order, so a D tells you to tune up, while an F or G means you should tune down.
Play the next string down and take a gander at your tuner. It should read the note as being an A, but if it doesn't, the string is out of tune. Adjust accordingly.
Check if your D string is in tune by playing the next string down from A. Take a look at the tuner and, if the string is in tune, you'll see D. If not, you'll see another musical note. Adjust the tuning pegs until the tuner reads the string as sounding a D note.
Play the string that follows the D string (the G string) and note what the tuner says. If your tuner tells you the string is tuned to any note other than G, adjust the tuning pegs.
Hit the C string (the thinnest string on the six-string bass guitar) and pay attention to what your electronic bass tuner says about the sound of the note. More than likely, your tuner will say that your C string is really tuned to D or perhaps B--in which case, adjust those tuning pegs by either raising tension (tuning up) or decreasing tension (tuning down).