As Toby Jaffey said in his post:
You need to ensure the strips are clean and dust free, line them up perfectly then maintain pressure. Be careful not to stretch or bend the strips while installing them as the contacts are often very small pitch.
This is probably the way to go. I would comment that in the picture it does not look like the contacts are very small pitch. I disagree with the other posters who have suggested using graphite to enhance the connection. I would not put graphite or any other conductive powder/substance on the pwb or connector.
In order for electrical contact to be made, pressure must be continuously applied to the LCD/elasto/PCB "sandwich". This is normally accomplished by the case, which is screwed together, pressing in on the structure from both sides.
The following procedure should work if you can pull it off. You might need help from a friend or some kind of jig...
- Sandwich the elastomeric connector between the LCD connector and the board pads. You will need to keep enough pressure on the sandwich to keep the connector from wiggling around.
- Screw the case back together while making sure the LCD/elasto/PCB sandwich doesn't come apart. This is assuming that you still have the case, and you will be reassembling it...
- Test it
Note: the LCD connector is not visually distinctive. Referring to the photo you have attached, I would guess that it is the translucent region at the bottom of the LCD module. You can just make out the "ghosted" strips which are possibly electrically conductive. Or maybe the clear strips are. You will figure it out. You probably could use an ohmmeter to test continuity if you are very careful and gentle. Anyway, the black squares on the connector edges are the conductive parts of the elasto connector, and should be lined up with the PCB pads and the conductive LCD "pads".
I once took apart an electronic guitar tuner which was having display problems, and to my great surprise encountered one of those elastomeric connectors. I had never seen one before. It totally freaked me out when it fell off and I could not see any adhesive or other fastening agent to reattach it with... but using the above procedure I put it back together and it's working, once again...