The entrance of the tunnel is directly situated along the M20 at exit 11a just North of Folkestone. It can also be accessed by the A20 (Ashford Road) which join the M20 at exit 11 and exit 12. This would the solution if you wish to join the tunnel by foot.
Bear in mind that even if some people might seem resistant to the idea of helping someone to cross the Channel into France, many others won't be stressed with that idea, which is not exactly the case on the reverse journey. The crossing into the tunnel is paid per car, so a hitch-hiker does not incur any extra cost to the driver. The check-in is mostly electronic, so the driver doesn't need to speak with any ticket collectors or such who might conceivably ask questions re: hitch-hikers.
There are many possibilities to try, what worked for me best was the last petrol station just before the port. It is just next to a traffic light and everybody comes pass here and might have to slow down or even wait for a minute at the traffic light...
I stood just next to the street, a few meters from the traffic light and the road going left away. I had a sign (a4 )stating "Ferry?". I had once to wait around 30 min and once just 5 min, in order to get a lift on the ferry, over the channel. Normally, people pay for whole cars, so it does not matter when they are more then stated on their booked ticket (the amount on their is more for safety reasons).
If you are once on the ferry, you can try and ask around in order to find somebody who goes in the direction you want to travel on. Good luck with that! I have not succeeded in this, yet... If you know good strategies, please let me know about them. If you have to hitchhike on in Calais, check out the Calais entry here.
The crossing takes about 40 minutes, once in the train it is possible to simply walk along the carriage to other cars and spot a car that might go direct to your direction and simply ask the drivers. Then you can catch a ride further into France, Belgium, Germany, the Netherlands just by swapping cars.
Maidstone Services is the only services located along the M20, at exit 8, it is most likely the spot to reach when hitching towards the M20. From there, you can show a sign or ask the people. Remind them that the Tunnel crossing is paid per car.
At the tunnel entrance directly, of course logic would show that if you try to hitch at the booth itself it is more likely that they will boot you out of there. So keep discrete and away of any of this potential trouble. The best spot seems to be at the exit 11a, coming from the Ashford Road on-ramp and standing along the road just before being beneath the viaduct. There is a wide shoulder and with a sign, you can be seen by the cars coming from the highway and they can pull aside if they wish.
Of course, it might end up being a jeopardy and what works quickly for some might not for others. Belgians seems more keen on picking people over the tunnel, so if you show a big sign marked 'B' you might get more lucky than simply Calais.
By standing nearby the viaduct, you cannot be seen from the toll booths (which are 800 yards away), there is no camera (surprisingly) and you are still somehow nearby the local road. Maybe the police would not be keen on letting you continue, but they can only find you out if they happen to be passing by.
The French authorities are usually pretty easy on passport checking and depending on what car you are in, you might end up not having to be controlled whatsoever.
Outside the Tunnel
Upon arrival in France while leaving the tunnel, there is a Shell petrol station located right at the exit before cars reach the motorway. This place could be the right place to find another ride further if you didn't manage to find the right one inside the train.
Direction England, (Folkestone)
Do NOT try to hitchhike at the tunnel entrance [edit - see below, highly debatable]. The place is huge, cars are fast and most drivers are confused. Also, the staff doesn't like hitchhikers and might threaten you to call the police if you don't leave. If you don't get a lift from outside of Calais to England, try the ferry instead. It's much easier.
Jass hitched the tunnel entrance in August 2010. Stand at the split off from the two roads behind a kind of arrow indicator. Staff can't see you so well and cars are slowing down to figure out which lane they need to be in. Have a sign for wherever you're going (UK and underneath your destination) and then FREE / GRATIS/ GRATUIT! Jass waited twenty minutes and a direct ride to Cambridge. Perfect and so much quicker than the ferry. Just be careful and discreet. Remember they'll be other hitchers here and we don't want to attract bad attention!