Apply powder if necessary
Apply some talc or baby powder to the seal where it is sticking. This will prevent the new seal from catching.
Flatten Seal with screwdriver
Use a screwdriver to flatten the seal as you close it. This will allow the seal to flatten. Leave the door shut for around 2 hours after doing this to allow the seal time to mould into the squashed up state on a permanent basis.
If there are no screws holding the liner in, then you will most likely need to pull the seal out with a little force. Be sure to pull in the same direction as the liner, to make sure that you do not tear the insulation in the door.
Rub some talc or baby powder on the corner that it is catching, both on the seal and the surface it is catching on.
Put a small piece of weather seal under the seal, about 10mm from the corner. This will help to bridge the gap between the two different heights. The poor design of many models of fridges means that a seal has to perform miracles to seal between two different levels because of the white plug thing they put in the corners.
As you are closing the door, wedge a screwdriver in to flatten the seal as you close it.
Heat the corner of the seal with a hairdryer to assist it moulding into shape.