Brief Introduction to Photoshop
Here is the screenshot of
Photoshop Interface:

Tools and Options Panel
Open your Photoshop. If you don't see Tools Toolbar already then go to
Window > Tools
Below is the screenshot of the
Tools panel. If the tool has a small trianlge at the bottom corner it means it has more than one tools. To see these options just click on the tool and hold your mouse for a few seconds, and you will see the options on the popup window as shown below.
Let's go through one tool from each group and their functions. The letters inside the brackets are the shortcuts for the particular tool, when you are in Photoshop and press
V for example it would select the
Move Tool.

Move Tool (V): Is used to select and move images (objects) on any active layer.

Rectangular Marquee Tool (M): It is used for making selection on the image (objects) on any active layer.

Magic Wand Tool (W): Used for making selection (similar colors at once for example)

Crop Tool (C): Used for cropping images

Polygonal Lasso Tool (L): Used for making free selection as you go.

Slice Select Tool (K): Used for selecting slices

Patch Tool (J): Used for correcting images

Brush Tool (B): Used for drawing freehand

History Brush Tool (Y): Used for restoring specified history state

Clone Stamp Tool (S): Used for selecting a source and copying (drawing) it in another place

Gradient Tool (G): Used for making gradient effect on images

Eraser Tool (E): You are right, this tool is used for erasing

Dodge Tool (O): Used for making images lighter (And Burn tool makes the opposite - darker)

Horizontal Type Tool (T): Yes used for inserting text to image

Path Selection Tool (A): Used for selecting the active path

Custom Shape Tool (U): Used to insert pre-specified (ready) shapes to image

Pen Tool (P): Used for creating vector shapes

Eyedropper Tool (I): Used for selecting color

Notes Tool (N): Used for inserting notes on the image

Zoom Tool (Z): Yes used for zooming in or out

Hand Tool (H): Used for dragging image when you are in the zoom in state
Options Panel
As you see below from the screenshot below,
Options Panel is highlighted with light-red. Whenever you switch from one tool to another,
Options Panel will change accordingly. Currently as you can see
Brush Tool is selected in the
Tools panel, and in the
Options Panel you can see the properties of the
Brush Tool, namely : Brush Size (Type), Mode, Opacity and Flow.
Just remember to look up to the
Options Panel when you choose a particular tool, because sometimes if something is selected or unselected in the
Options Panel, you might not be able to use that particular tool properly. For example Opacity of the color might be set to "Zero" in the
Options Panel, in that case anything that you draw would not show up since 0 means invisible.
