Hi,
One way is to look at the flight search forms on the sites you want to feature. View the source code in your web browser and search for the "<FORM". There may be more than one form in the code. I would do this even if the site is like Expedia and uses the GET method rather POST.
You'll need to do a bit of work sorting out the variables, eg. for the departure airports Opodo use B_LOCATION_1 and ebookers use DEP. They accept IATAs 3 letter airport codes. The format for dates varies between sites.
You may need to do some research on HTML forms as you'll need to understand how SELECT, RADIO, CHECKBOX, etc. work.
You can then create a URL or build your own forms to post data to the websites. Post the variables from your original form on your website to these.
We've done this on our site farebuster.co.uk eg. you want a
fight to Geneva Clicking on the orange "Book with..." takes you to a form
flights from LHR to GVA This form posts flight searches to Gate62.com
We've also done this with Opodo and ebookers on another site. I'm in the process of working on Airline Network. We've got the code for other sites as well.
You'll need to keep an eye out if any of the websites change their forms. If you want an easy solution I'd use something like Affiliate Future's flight search or Kelkoo's flight search (on tradedoubler).
All the best,
Nick