Purchase a basic book on percussion note reading from a music store. You can also find the information on line, free of charge (see Resources). Learning the basics of reading drum notes isn't difficult, but it's a good idea to keep a book handy to refer to as you master recognizing note rhythms. Even a beginner's guide to reading music notes will work, since much of the information is the same as it is for drum notation.
Learn the music staff as it applies to drum notation. Drums use the same music staff as other instruments, but instead of indicating note names and pitches, the five lines and four spaces of the staff indicate specific drums and rhythms. The first line of the music staff is the bass drum. The space below bass drum indicates ride cymbals. The third line belongs to the snare drum. Notate tom-toms on the second, third and fourth spaces, from the lowest to highest. Hi-hat cymbals are on the first space above the top line on the staff.
Practice writing drum rhythms on blank sheet music paper. Write whole notes first, just to keep it simple, then play them to hear how they sound. A whole note is a circle drawn on the line or space of the drum you play it on. A whole note means you will hold the note four beats before playing the next note. Place a whole note on the bass drum line, a whole note on the snare, a whole note on the lowest tom, and another on the bass. Play this rhythm, hitting each drum on beat one and holding it four beats before moving on.
Study music rhythms until you get a feel for the different note values. In addition to whole notes, there are half notes (two beats), quarter notes (one beat), and eighth notes (a half a beat). These values are all in 4/4 time, also called common time. The 4/4 time signature means there are four quarter note beats to a bar of music. You create those beats by combining different note values.
Play a half note and quarter note pattern. Draw a circle with a short stem on the right side. This is a half note. Place it on the bass drum. Draw two quarter notes on the third line (snare). A quarter note has a circle colored in and a stem on the right. Half notes equal two beats and quarter notes are one beat each. Play the rhythm to see how it sounds. Strike the half note on the bass line on beat one and hold it for two counts, then strike the quarter notes on beats three and four.
Your beginning books or online resources will give you all the possible musical note rhythms. Keep your guide handy until you have mastered counting and playing the rhythms.