Using the Dailymotion API
https://api.dailymotion.com/video/VIDEO_ID?fields=field1,field2,...
Replace field1,field2 with
thumbnail_large_url (320px by 240px)
thumbnail_medium_url (160px by 120px)
thumbnail_small_url (80px by 60px)
This API request does not require any Access Tokens.
Example :
https://api.dailymotion.com/video/xjfn0s?fields=thumbnail_small_url
This HTTP request returns a JSON data with the image link of the video. For processing JSON data check PHP Manual - JSON Decode
EDIT
As suggested by Ravi using
http://www.dailymotion.com/thumbnail/video/video_id
is pretty straight forward. But different resolution images use the API