Microsoft Paint: Tools
Curve Tool

The Curve tool is trickier to use than the Line tool. It can be difficult to learn how to use, and it is difficult to explain. Your best bet is to experiment with it, but be patient, because it will take a lot of getting used to before you get very good at making curved lines that are the shape that you want.

Like the straight Line tool, the Curve tool can make lines in various thicknesses and colors.

Try experimenting with various techniques for making lines. Try clicking and dragging to make one kind of line, or clicking and releasing two endpoints. Click a third point to determine the curve. Try dragging an already drawn, but still active, multi-point line to distort its curve.

The Curve tool can be very frustrating, especially for beginners, especially since the Undo command can only be used to undo the last change you've made to your image. Just keep practicing!

Example:

I made these curved lines using the curve tool.  The green line has two bends in it (the maximum).  The red line just has one curve.  Just draw a line like you would with the straight line tool, then click and drag to bend the line and make it curve.  The grey loop was created by employing a single click to start a point, then dragging the curved line open to create a full loop.

Microsoft Paint: Tools
Shapes

The Shapes tools are all very similar, so we’ll look at them all at once.

Rectangle
The Rectangle tool draws three types of rectangles: outline, filled with outline, and filled without outline. The interior of the outline rectangle is transparent, whereas the filled types fill the rectangle with the background color. To draw a rectangle, click on the tool, then click a point on the image where you want one corner to be, then drag diagonally and release the mouse where you want the opposite corner to be.
Tip:  To create a square shape, hold down the Shift Key as you draw the shape.

Example:

Here's a cool composition I created using only the rectangle tool.  Overlapping rectangles, filled rectangles, outlines, different colors... It creates a nice effect.

Polygon
The Polygon tool is similar to the rectangle, but works a bit differently. To create a polygon, activate the tool from the tool bar. Then, click on the image wherever you want your first vertice to be. A vertice is like a corner. Draw the edges of the shape like you would use the Straight Line tool, then simply connect the last edge to the first vertice and the shape will finish. You have to be pretty precise, though. If you just miss by a few pixels, the shape will think that you want to continue adding sides to the polygon.
Tip:  You can constrain the angle of the line segments of the polygon to 45 degree increments by holding down the shift key as you click to create the next vertex.

Polygons are great for all creating all kinds of irregular shapes.  Unfortunately, it's more difficult to draw a regular polygon, because you have to do each side of the polygon free-hand.  But it is still a pretty useful tool.  For instance, you can see here how you can use many irregular polygons to create a tile mosaic sort of look.

The Oval Tool works much like the Rectangle tool. The only difference is that since there are no corners, you will need to guess where the corners would be in order to place your oval where you want it to go. Imagine that the oval you are drawing is being "hugged" by a rectangle that goes around it. Like up the top-most and left-most peaks of the oval’s curve to guess where the corner of the imaginary rectangle is and click there. Then, drag down to where the bottom-most and right-most peaks of the oval’s curve would be, and click again. Your oval should be about the right size and in the right position if you estimated it correctly. It can take some practice.

Like the other shapes, you can create ovals that are just empty outlines, filled outlines, or filled with no outline.
Tip:  To create perfect circles, hold down the shift key as you draw the shape.

Example:

Here's a picture I did in just a few minutes using a number of oval shapes as well as some of the other drawing tools.  Notice how I used overlapping ovals to achieve a sense of perspective with the car's wheels, and for the shape of the car's body itself.  I also overlapped ovals to create the crescent moon effect.  I also used the Curve and Line tools for some of the details, the Fill tool to fill in spaces with color, and the Airbrush tool for the exhaust.