Moving around the Scene
The mouse selects objects by default.
The Left button will attempt to cycle through all the objects under the cursor, it's not really that good at it and in complex scenes it's best to use the Hierarchy to select objects.
The Middle button moves the scene.
The Right button rotates the view around the viewer.
Press Alt and the Left mouse button will rotate around the currently selected object.
Alt+Left Ctrl + Left mouse will move the view
Basic tools in Unity
From the left
The "Hand Tool", will change to an "Eye" when holding down Alt. This is the tool to use to navigate around
The "Move Tool". Selects and moves objects around the scene.
"Rotation Tool" gives the tools to rotate objects
"Scale Tool" enables scaling of objects
"Rect Tool" surrounds objects with a rectangle which allows for dragging an object and scaling them using a rectangle, mainly useful for 2D operations.
A Combined tool, allows movement, scaling and rotation in one.