Monsanto is a little out if the way, so your best bet of getting there is by car as I should imagine public transport is not to frequent!
Monsanto is also pretty high, so should you try and go by bike, you will be in for a lot of hills and climbing.
However going by car brings on its own difficulties. Parking is rather hard to come by once you get there. As yoy can see from this picture, we had to be a little creative with our parking, finding a bend and squeezing it in.
Monsanto is in the municipality of Idanha-a-Nova in the Beira Alta. Monsant is 321 Kilometres from Oporto and 300 Kilometres from Lisbon. Get on the N240 from Castelo-Branco towards Spain, and then approx halfway to Spain, turn off and follow the signs.
Monsanto is pretty small, and parking is pretty difficult, and the roads are very very narrow and have very tight bends. To look around the town, the only way to do it is to park wherever you can find a space, and then get out and walk.
If you want to go up to the castle, you must walk, there is no other option, and there is a little bit of climbing to do to. The views are well worth it however, and when you are coming back down, you can really drink in th view (the view is mostly behind you as you go up ;-) ).
As you can see the streets are to small for cars and a bike would be no good going up and down the stairs so the best thing to do is walk.
Bring a good pair of hiking shoes with a good sole on them as there is loads of walking to do.
I can't say enough good things about the highways in Portugal - they far exceeded my expectations! Whether they were super divided 4-lane affairs, normal highways or even what might be considered back roads, the quality was always very high. In the entire 2500-km trip, we only encountered one highway (in the far northern Minho region) that was very bumpy and had numerous potholes (but they were working to fix even that!). This is a scene from what, on the map, appears to be a little-used back road. We took it as a scenic way to reach Monsanto because we prefer to travel those routes unless we are in a time pinch to reach a particular place. The scenery was great, the road was smooth and well sign-posted and there was very little other traffic hurrying us along. Perfect!