There are several (non-free) parking spaces on the route to the 3-country point (coming from the dutch side) but if you ignore them all and just drive past the tower (at the 3-cp) there is a free parking spot right behind it on the belgian side. It is small but since people don't stay for very long you don't have to wait an awefull long time.
There is a regular bus service between Maastricht and Vaals, the South Limburg Veolia #50 which goes on to Aachen. Buses leave from stand D, just outside the train station, approximately every 15 minutes with a journey time of about 50 minutes. The main Vaals bus stop is on the high street, Maastrrichterlaan, and is a couple of minutes walk from the road that leads up to Vaalserberg.
A one-way ticket is 5.50 Euros (July 2010) but if returning, or travelling further around the area, the day ticket (dagskaart) is excellent value at 7 Euros and allows travel on all South Limburg Veolia services. Tickets can be bought from the driver and correct change is appreciated.
...you can take the bus. There's an hourly bus service, the Veolia #149, which runs between Vaals bus station and the Vaalserberg summit. If you've come from Maastricht and have bought the day ticket then this is valid on this service.
Here's the route plan for bus Veolia line 50 from Aachen main station (Hauptbahnhof) to Vaals:
Then from Vaals to Tentstraat 81 (that's your stop). From there a 3 minute walk to Drielandenpunt (Gemmenicherweg 35), it's a 6 minute ride with bus Veolia 61.
Mind you, best check with www.aachen.de (email them!), I've never done that route with bus.
From Vaals, you could use www.9292ov.nl (that's for all public transportation in The Netherlands).
For translation to use this VT tip:
Don't take the Veolia 54 and then Veolia 61 at 58 minutes past each hour, because that trip takes 45 minutes instead of 6 !
If you have no car to travel with, you will most likely come either from the direction of Maastricht by bus or from Aachen by bus. In Aachen there are several buslines going to "Vaals Grenze", some of them are 25, 33, and 65. They will all take you to the border (or even beyond). It costs €1,80, one way. Best way to get on is in front of Elisenbrunnen (Yellow building with columns in the centre).
Coming from Maastricht you should take the interliner, which costs €3,50, one way, and it leaves from the trainstation. The Interliner takes about 40 minutes.
There is also a local bus going to Heerlen, where there is a trainstation.
Interliner Bus 420 leaves every half an hour from Maastricht, Vaals to Aachen. But you should expect bus once per hour if you leave very early or very late or during weekends. This is Europe! :-)
Interliner Bus leaves every 17", 47". Last bus back from Aachen is 00:07. But 23:07 on Sunday. Cost: euro8.10 return (train discount card can be used for interliner bus with 40% discount)
You can get off at Vaals, then get on later to Aachen. The ticket is valid during the day!
VVV tourist office is just opposite to the bus stop of Vaals.
Upon arrival at Vaals bus stop (opposite to the VVV tourist office), walked backwards and turn left at the first street, then walked 20min till you see the T-road, then turn left again, walked about 15min, then you will see sign of the 3 country meeting point. Following the sign and you won't miss it.
Vaals is located west from Aachen Germany, between this two cities is only the state border.You just need to find the bus that goes on the Vaalser strasse. Local bus company is called ASEAG.