One of the first lessons for a beginning bass guitar player is how to learn the names of the notes on a bass. You can play by ear, follow bass tabs, or mimic a lead guitarist, but at some point you really need to know the notes to advance your skills. Fortunately, they are very easy to learn.
Note Name Basics
The vast range of musical pitches is split up into units called octaves. An octave is the distance between two notes that have the same pitch (such as A and the next A). For example, play an open string on your bass, and then play the note you get from putting a finger down on the 12th fret (marked with a double dot). That note is one octave higher.
Each octave is divided into twelve notes. Seven of these notes, called the "natural" notes, are named with the letters of the alphabet, A through G. These correspond to the white keys on a piano. The other five notes, the black keys, are named using a letter and a sharp or flat sign. A sharp sign, ♯, indicates one note higher, while a flat sign, ♭, indicates one note lower. For example, the note in between C and D is called either C♯ (pronounced C-sharp) or D♭ (D-flat).
As you may have noticed, there are too many natural notes to have a sharp/flat in between every pair of neighbors. B and C natural have no note in between them, and neither do E and F. On a piano, these are the places where two neighboring white keys have no black key in between. So (except in advanced music theory) there is no such thing as a B♯, C♭, E♯, or F♭.
To recap, the names of the twelve notes in an octave are:
A, A♯/B♭, B, C, C♯/D♭, D, D♯/E♭, E, F, F♯/G♭, G, G♯/A♭, A...
Note Names on the Bass
Now that you know the note names, it's time to look at your instrument. The lowest, thickest string is the E string. When you play it without any fingers down, you are playing an E. When you play it with your finger down on the first fret, you are playing an F. Next is an F♯. Each consecutive fret raises the pitch by one note.
The simplest way to learn note names is to continue playing the note on each fret and naming it aloud as you go up. Notice that when you reach the fret marked with a double dot (12th fret), you've come back around to E again. Try this on all the strings. The next string is the A string, followed by the D string and the G string.
You may have noticed that certain frets are marked with single dots. These are good reference points to memorize first. For example, if you are going to play a song in the key of C, it will be useful to immediately know that the first dotted (3rd) fret on the A string is a C. Work out what notes the dots are on each string. The dots up past the double dot are the same notes as the ones below, only an octave higher.