Right ok, this is the first time I've attempted to write a tab by ear, so if it's wrong, well yeah...

At the start cover the strings without pressing down and strum up then down up then down on the low E and A string.

Verse 1

|------------------------------------------------------------------|
|------------------------------------------------------------------|
|----------9-9-9-9---------9-9-9-9---------7-7-7-7-9-9-9-9-9-9-----|
|--7-7-7-7-9-9-9-9-7-7-7-7-9-9-9-9-4-4-4-4-7-7-7-7-9-9-9-9-9-9-----|
|--7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-4-4-4-4-5-5-5-5-7-7-7-7-7-7-----|
|--5-5-5-5---------5-5-5-5---------2-2-2-2-------------------------|

|------------------------------------------------------------------|
|------------------------------------------------------------------|
|----------9-9-9-9---------9-9-9-9---------7-7-7-7-9-9-9-9-9-9-----|
|--7-7-7-7-9-9-9-9-7-7-7-7-9-9-9-9-4-4-4-4-7-7-7-7-9-9-9-9-9-9-----|
|--7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-4-4-4-4-5-5-5-5-7-7-7-7-7-7-----|
|--5-5-5-5---------5-5-5-5---------2-2-2-2-------------------------|

Chorus, the bit where Billie Joe goes "OOOOOOOOOOOOOOOOOOOOOOOOOOOOHHooooooooooh oh no"

|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--7-7-7-7-----------------7-7-7-7-----------------7-7-7-7--------------------|
|--7-7-7-7-5-5-5-5-7-7-7-7-7-7-7-7-5-5-5-5-7-7-7-7-7-7-7-7-5-5-5-5-7-7-7-7----|   Let Ring after final chord.
|--5-5-5-5-5-5-5-5-7-7-7-7-5-5-5-5-5-5-5-5-7-7-7-7-5-5-5-5-5-5-5-5-7-7-7-7----|
|----------3-3-3-3-5-5-5-5---------3-3-3-3-5-5-5-5---------3-3-3-3-5-5-5-5----|

Verse 2

|------------------------------------------------------------------|
|------------------------------------------------------------------|
|----------9-9-9-9---------9-9-9-9---------7-7-7-7-9-9-9-9-9-9-----|
|--7-7-7-7-9-9-9-9-7-7-7-7-9-9-9-9-4-4-4-4-7-7-7-7-9-9-9-9-9-9-----|
|--7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-4-4-4-4-5-5-5-5-7-7-7-7-7-7-----|
|--5-5-5-5---------5-5-5-5---------2-2-2-2-------------------------|

|------------------------------------------------------------------|
|------------------------------------------------------------------|
|----------9-9-9-9---------9-9-9-9---------7-7-7-7-9-9-9-9-9-9-----|
|--7-7-7-7-9-9-9-9-7-7-7-7-9-9-9-9-4-4-4-4-7-7-7-7-9-9-9-9-9-9-----|
|--7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-4-4-4-4-5-5-5-5-7-7-7-7-7-7-----|
|--5-5-5-5---------5-5-5-5---------2-2-2-2-------------------------|

Chorus

|-----------------------------------------------------------------------------|
|-----------------------------------------------------------------------------|
|--7-7-7-7-----------------7-7-7-7-----------------7-7-7-7--------------------|
|--7-7-7-7-5-5-5-5-7-7-7-7-7-7-7-7-5-5-5-5-7-7-7-7-7-7-7-7-5-5-5-5-7-7-7-7----|  
|--5-5-5-5-5-5-5-5-7-7-7-7-5-5-5-5-5-5-5-5-7-7-7-7-5-5-5-5-5-5-5-5-7-7-7-7----|
|----------3-3-3-3-5-5-5-5---------3-3-3-3-5-5-5-5---------3-3-3-3-5-5-5-5----|

Outro I'd call it

|-----------|
|-----------|
|-----------|
|--7-7-7-7--|
|--7-7-7-7--|
|--5-5-5-5--|