blue means that the piece is 'grounded', it has the best structural support. from there how well the piece is supported goes from shades of green to to yellow to orange to red. beams can be uses to increase support, as well as some environmental objects like trees. if a piece is not supported from a piece below it, it's color will show how much support it has... so if you have a floor piece that's blue and attach a wall to it the wall will be dark green. if you place another wall on top it will be a lighter shade green. if you put a roof on the 2nd wall it will be a lighter green and so on. if you kept extending roof pieces eventually they'll have too little support and will be a dark red and just break upon placing them, unless you add a support beam coming up from the ground. also if you went back to the first wall you built and removed it, everything above it would lose that support and fall apart.
pieces should snap together edge to edge without having to push shift or control. sometimes it helps to build yourself a scaffold to get a better view of the piece your snapping to.
one other thing, currently (and this may change in later updates) immediately after you initially place a piece it takes a moment to update the stabilities of it and the other pieces it attaches to, so if you're fast you can place pieces that normally wouldn't be able to be placed.