I'm pretty sure this is exactly how Tegan plays it:

Standard tuning
Chords are basically A, G and Bm but played with the top 2 strings open instead of as a 
bar chord.
Not sure if these have technical names so I'll write them as A, G and Bm but they are 
played like this:

A = 577600    G = 355400    Bm = 799700

So instead of barring with the index finger, fret the bottom E string with your thumb so 
the top 2 strings are open.

Majority of the song is just alternating from A to G. Take your hand completely off 
while changing chord and put in an up/down strum of the open strings in between, rather than 
sliding up and down.
Then for "so... it's been so long since you said..." it's Bm, G, A.



The Ocean - Tegan and Sara

A                                          G
When you wake what is it that you think of most?
                                           A
When your bed is empty do you really sleep alone?
                  G
If I imagine you, body next to another
A                                       G
All around me, new love and it makes me sad
                                           A
All around me, feel assured that you'll be back
                  G
If I imagine you, body next to another

A
Stop crying to the ocean
G
Stop crying over me
A
Stop worrying over nothing
G
Stop worrying over me
Bm           G                    A
So it's been so long since you said,
                                                            G
"Well I know what I want, and what I want's right here with you"

On the drive back here, I was worrying over nothing
On the drive back there, tears spilling over something
When I imagine you, body next to another
In the door, and you're there, and you're sorry for the fright
In the door, can I hear you saying you don't wanna fight?
When I imagine you, body next to another

Stop crying to the ocean
Stop crying over me
Stop worrying over nothing
Stop worrying over me
So it's been so long since you said
"Well I know what I want, and what I want's right here with you"
it's been so long since you said,
"well I know what I want, and what I want's right here with you"

In a flash it's back to you, just brought attention to the mess
In a flash, you're on top, begging me to understand
If I imagine you, body next to another
You drop in for a minute and I'm sorry that I didn't
Drop in sooner just to see you and to see what you've been doing
If I imagine you, body next to another

So it's been so long since you said,
"Well I know what I want, and what I want's right here with you"
it’s been so long since you said.... repeat til the end