I found the chart at http://patatafelice.com/downloads/italian-cheat-sheet-v2.png to be really helpful in memorizing the conjugations of the verbs. Mostly how ive been remembering it is
I Io -o so if its a phase about 'I' the verb will end in an O, so leggo
You tu -e if its a sentence about a singular you it will end in E, so legge
He/She Lui/Lei can end in -a, -e, or -e depending on if the conjugated verb ends in -are/-ere/-ire. For example leggere is the conjugated source of to read, so this will conjugate as legge instead of the -a it would for an -are verb. to drink is actually an irregular verb(if you look at the image, the second column, imperfetto) because because to drink is just 'bere' and while it ends in ere it needs a couple extra letters to flush out the ending, otherwise 'i drink' would just be 'bo' and thats far more confusing.
We Noi -iamo so 'we read' is 'leggiamo'
You Voi -ete Y'all becomes 'leggete'
They Lono -ono (or -ano if its an '-are' verb) is 'they read' so the word would be 'leggono'
Because the endings specify the 'who' you are talking to, the Io/Tu/etc will oftentimes get dropped.
Hope this helps!