If you plan to drive to Weesenstein, make sure to avoid rush hours in Dresden. The roads Dresden - Heidenau - Pirna are usually one single traffic jam.
Anyway, from Dresden drive to Heidenau (B 172). In Heidenau take the turn to Weesenstein - Glashütte - Altenberg. From my experience it takes about 30 minutes from Dresden city centre to Heidenau, another 10 minutes to Weesenstein.
Parking right below the castle or on the bigger parking before you cross the river (left side). Either way, you must pay a fee of about 2 or 3 Euro.
See also the map in pic 4 of the previous tip ("Public Transportation").
Assuming you will go to Weesenstein from Dresden, I highly recommend public transportation. Every half hour regional trains (S-Bahn No. 1) run from Meissen to Bad Schandau via Dresden-Hauptbahnhof (and other stops in Dresden). Take one of those (preferrably those which leave Dresden Hauptbahnhof at the full hour) to Heidenau, where you change for the train to Weesenstein (regional trains to Altenberg). Travel time Dresden Hbf - Weesenstein is about 25 minutes.
From the train stop in Weesenstein it is (roughly) a 10 minutes walk to the castle, it's signposted. See pic 4.
Fares and rules of the public transportation network VVO apply: Weesenstein is located in the zone "Pirna". From Dresden you need a ticket for 2 zones (Dresden + Pirna). One zone costs 2 Euro, the two zones are 3.80 Euro. If two adults (plus max 4 children to 13 years) are travelling together you better purchase a family day ticket.
Weesenstein can easily be reached by train. The village is a stop along the local line from Heidenau to Altenberg which runs hourly. From Dresden, take the S-Bahn (S1 direction Schöna/Bad Schandau) to Heidenau and change there.
Warning: Check the timetable carefully, especially on weekends, because not all trains run daily and the nearest pub to spend an extra hour in is quite far away in the centre of the village. (Speaking from experience...)