When you leave the Eurostar train at Ashford International Station, there is a walkway through to the domestic section where you can catch a train to Dover Priory Station. When you get to Dover Priory it would probably be best to take a taxi for the short journey the Port (do not know the costing for taxi).
As for costings I do not know your time of travel and you need to be aware that it is a commuter route so could be busy during rush hours. I have just done a dummy run for midday next Tuesday on the link below which shows at least 3 train per hour at under 9 GBP. You would need to put your own timings in to get more accurate information. You can buy your ticket at Ashford on the day.
To get from Dover to London you have the choice of three different routes. You can take a look at each, as getting to your final destination in London might be easier from one of the terminal stations than the other two:
Dover Priory to London Victoria : takes about 2 hours, two trains every hour weekdays and Saturdays, one train every hour on Sundays and Holidays
Dover Priory to London Charing Cross (also stops at London Bridge and Waterloo East) : takes 1hr 50 minutes with at least two trains every hour weekdays, one train every hour Saturdays, Sundays and Holidays.
Dover Priory to St Pancras via the high-speed line (more expensive that the first two options) : takes 1 hour 10 minutes,. one direct train each hour every day plus additional trains at busy times.
You can download the timetable from this webpage
then click on 'Mainline1' which is the summary of all trains between London, Folkestone, Dover and Canterbury by all three routes. Note that there are no seat reservations available on SouthEastern trains but since almost all the trains start from Dover you would be very unlucky if you didn't get a seat!
When you arrive from Paris on the Eurostar, you will pull into platform 3 or 4. There is a lift down to the connecting underway which connects to the domestic trains.
Dover trains ( usually) leave from platforms 5 and 6, and again, there is a connecting lift to take you back up to the platforms
There are TV screens at the intersections telling you which platforms the various trains leave from and arrive at... so you don't end up lugging your bags to the wrong platform.
From London back to Dover, the fastet ( +more expensive) is by the new high speed link. This is served in London, only from St.Pancras,(do not attempt to go to Ebbsfleet) but you can take much slower trains from Victoria.
Occassionally there are engineering works, which delay, re route or even cancel trains. This work usually takes place late at night or at week ends, and (so far) hasn't applied to the high speed line. For further information, (additional to the web sites other posters have given you) see www.southeasternrailways.co.uk, you can download a time table from this site.
-:- Message from TripAdvisor staff -:-
This topic has been closed to new posts due to inactivity. We hope you'll join the conversation by posting to an open topic or starting a new one.
To review the TripAdvisor Forums Posting Guidelines, please follow this link: http://www.tripadvisor.com/pages/forums_posting_guidelines.html
We remove posts that do not follow our posting guidelines, and we reserve the right to remove any post for any reason.