There are many ways to play this, but this is how to do it with standard tuning.
Intro (Come in after main guitar riff with drums, etc)
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------| x2
E ---------6-6-6-6-4-4-4-4-4-4-4-4-|
Intro (continued)
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------|
E ---------6-6-6-6-8-8-8-8-4-4-4-4-|
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------|
E ---------6-6-6-6-4-4-4-4-4-4-4-4-|
Verse
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------| x3
E ---------6-6-6-6-4-4-4-4-4-4-4-4-|
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------|
E ---------6-6-6-6-8-8-8-8-8-8-8-8-|
Refrain 1 (I wanted more...)
G ---------------------------------|
D ---------------------------------|
A ---------------------------------| x3
E -1-1-1-1-4-4-4-4-8-8-8-8-8-8-8-8-|
G ---------------------------------|
D ---------------------------------|
A ------------------------5-5-5-5--|
E 1-1-1-1-4-4-4-4-3-3-3-3----------|
Verse
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------| x3
E ---------6-6-6-6-4-4-4-4-4-4-4-4-|
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------|
E ---------6-6-6-6-8-8-8-8-8-8-8-8-|
[ Tab from: https://www.guitartabs.cc/tabs/s/smashing_pumpkins/today_btab_ver_6.html ]
Refrain 2 (Pink ribbon scars...)
G ---------------------------------|
D ---------------------------------|
A -----------------6-6-6-6---------| x3
E -1-1-1-1-4-4-4-4---------6-6-6-6-|
G ---------------------------------|
D ---------------------------------|
A ------------------------5-5-5-5--|
E 1-1-1-1-4-4-4-4-3-3-3-3----------|
Pre-bridge (same as intro)
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------| x2
E ---------6-6-6-6-4-4-4-4-4-4-4-4-|
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------|
E ---------6-6-6-6-8-8-8-8-4-4-4-4-|
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------|
E ---------6-6-6-6-8-8-8-8-8-8-8-8-|
Bridge (I want to turn you on...)
G ---------------------------------|
D ---------------------------------|
A ---------------------------------| x3
E -1-1-1-1-4-4-4-4-8-8-8-8-8-8-8-8-|
G ----------------|
D ----------------|
A ----------------|
E 1-1-1-1-4-4-4-4-| Go right into ending
Ending (same as intro)
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------| x2
E ---------6-6-6-6-4-4-4-4-4-4-4-4-|
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------|
E ---------6-6-6-6-8-8-8-8-4-4-4-4-|
G ---------------------------------|
D ---------------------------------|
A -6-6-6-6-------------------------|
E ---------6-6-6-6-4-4-4-4-4-4-4-4-|