Despite the apparent simplicity of Don't Sit Down 'Cause I've Moved Your Chair, you'll still have to deal with a slightly awkward fingering if you want to get the right sound.
Play the open D5 chord with your second finger and use your first finger to play the E note that forms the main part of the riff. Play the descending line with your third finger, then use your first finger for the remaining notes. This fingering produces an uncomfortable stretch on the final note that may take a little time to master.
Make sure the A note on the third string isn't played too loudly. It should ring subtly in the background. Generally, this note sounds as you play the E note on the fourth string and on the descending notes. However, Alex Turner doesn't play it consistently throughout the song, so don't get too bogged down trying to copy it exactly.
Get the sound
Go for a clean tone with plenty of treble and be quite generous with the reverb. Use a guitar with a single-coil pickup in the bridge position. If you're using a guitar with a humbucker, you can try rolling off the bass to its lowest setting to get close to a singlecoil tone and to stop the sound from getting too woolly.