First make sure you have Snap to Grid off, or it will seem like you cannot move objects unless you are zoomed far out. When it's off you can move objects freely, instead of locked into the grid of invisible squares.
Toggle that by clicking the # looking square in the top tool bar. The one beside it is Snap to Angle, which works the same, but for the rotation angle the object is facing.
You do want Snap to Grid and Snap to Angle on when using objects that need to be aligned... Like building a house. But for placing small objects or NPCs, you want the freedom of them being turned off.

You move objects by selecting them and moving them with the mouse, but as you will have noticed you can only move on the X and Y axis, not the Z axis (up & down.)

Grab the object (hold the mouse button) and then hold Z on your keyboard also. Now you can move the object along the Z axis.

This also works for the X and Y axis, using the corresponding buttons on the keyboard.

You can also "drop" any object to the object beneath it (including the floor) by pressing F when it is selected.
Note that this doesn't work for all objects (like Lights) and can cause you to drop the object into places you don't want, so it's usually best used when you're already near other objects.
NPCs will usually fall down on the object below them when in-game, so it is OK if they float a little bit.

If you make a mistake you can hit Backspace to undo the last change you made. Not sure how many moves it remembers, but it seems to be a lot.

For very precise object placement, double-click on an object. You'll see the Position X,Y,Z and Rotation X,Y,Z. Use the little arrows beside them to move the object.
When done, close that window by clicking the red X at the top right corner. Do not press Save.


Some of that you might already known, just covering all the basics for movement

I didn't believe in astrology, and here I am getting advice from a subplanet

Thanks!

Unfortunately a lot of the links in the Tutorial Sticky no longer work - they point to old sites

This is http://1drv.ms/1JVKMkC - I used it for years - hope it helps

@Illuminiel, Excellent guide, that one! Never seen it before, but covers almost everything and its been explained wonderfully.

Wow, this is great. Thanks for sharing!