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Linear perspective is a wonderful tool discovered by Renaissance artists for making two dimensional art appear three dimensional.
Step 1. Draw a horizon line. Draw a dot for your vanishing point on the horizon line. It can even be off the page.
Step 2. Draw the vertical and horizontal lines that form the front edges of your form.
Step 3.Connect the ends of your front edges to the vanishing point.
Step 4. Draw any back edges that you want on your form.
Step 5.Erase any extra lines you don't need. Draw in any that are needed.
Step 6. Keep going.
Two point perspective is great for showing angles rather than head on. It's often used for cityscapes.
Step 1. Draw a horizon line. Draw two dots for your vanishing point on the horizon line. They can be off the page.
Step 2.Draw the vertical line that forms the front edge of your form.
Step 3. Connect the ends of your front edge to your vanishing points.
Step 4. Draw two verticals where you want the back edges of your form to be.
Step 5. Connect the new verticals to your vanishing points.
Step 6. Erase any lines you don't need.
Great for implying overwhelming height or depth.
Step 1. Draw a horizon line. Draw two dots for your vanishing points on the horizon line. They can be off the page. Draw another vanishing point either above or below the horizon line
Step 2. Draw a vertical line starting at the the far front corner your form and running to the vanishing point that isn't on the horizon. This will form the the front edge of your form. Draw another two lines on either side of that line, they will be your other "verticals".
Step 3. Draw your "horizontals" by connecting the corners of your front edge with the vanishing points on the horizon line.
This refers to how things lose saturation as they recede in space. Think of a distant mountain range; remember also that landscapes usually take on a tinge of the sky color as they recede.
Isometric perspective is most commonly used in pixel art.
It's similar to two point perspective, visually, but instead of having all lines converging towards a pair of points, all lines are parallel and form an identical angle with the horizon. This makes an infinitely repeatable system that's particularly convenient for gameplay.
While it's based on a 30 degree angle, the nature of computer monitors is such that 30 degrees gives a super ugly line, so the angle we use is more like 26.565 degrees, with the line going one pixel up and two across each time.
Curved perspective coming soon.