So now you're ready to actually get in and draw something in Blender. Creating a mesh will be your first step. For this, you want your 3D window to be in Edit Mode. You can hit the Tab key to reach Edit Mode from any other mode, or select Edit Mode from the first drop-down box from the left in the 3D window's header. Before we jump into it, let's go over some terminology, some of which you might remember from geometry class:
Vertex: This is the point at which more than one edge intersects in a geometric shape. In terms of the cube you see when you first open Blender, a vertex would simply be one of the corners where three lines meet. The plural is vertices.
Face: One of the object's surface areas. When you render an object in Blender, only the surfaces and their properties will be visible, not the vertices or edges.
Edge: The lines that form the boundaries of each face.
Mesh: The collection of faces, vertices and edges that create any particular object.
A Few Useful Hotkeys
A: Select/deselect all objects
CTRL + Space: Show/hide the axes arrows.
X: Deletes elements you select on the drop-down menu this gives you. Can also delete entire object(s) that you have selected.
Numpad 7: Lines up the 3D view so that it is perfectly lined up with the X and Y axes. Good for creating 2D images in Blender.
F: Used to create faces.
Creating Your First Mesh
For experimenting with meshes, I like to start simple. You can use the point-by-point method by holding down your control key and left-clicking at the points where you want your vertices to be. Blender will automatically connect each sequential vertex a line, as in the above pattern where I put down some random vertices. The orange edge is the one that is highlighted.
Each face can only be triangles or quadrangles, which is why I prefer to start with a simple mesh. Anything that has more sides than a quadrangle, or four-sided geometric figure, is called an N-gon, for N number of sides, and Blender doesn't support those.
To create a face, first hold down the Shift key and right-click on three adjacent vertices to select them. Then, hit the letter F. This creates a triangular face as in the image above. To create a quadrangle face, select four adjacent vertices and hit F. In 2D meshes, it's actually easier to not try to create the last edge of your geometric figure yourself when using the point-by-point method. You can just create two of the edges for a triangle or three for a quadrangle, select the vertices and hit F, and it will finish your geometric figure with an extra edge.
If your first 2D figure isn't the greatest, don't sweat it. You can manipulate it to make it look better by selecting one vertex, and then hitting G to access the Grab tool. Then, you can move that point by left-clicking on it and dragging it with your mouse. It will also drag the attached edges. When you have the vertex where you want it, left-click at any point off the vertex to release it. Right-clicking will release the vertex and put it back where it started. If you're working with just a 2D figure and you want it to stay 2D or you want better control, you can lock things to a specific axis by hitting X for the X axis, Y for the Y axis, or Z for the Z axis. Then, the point you move will only move along that specific axis. This is good for when you want better control of where your vertices will be positioned along each axis.
A Look At My Final Objects
What my objects look like after creating them and then playing with them with the Grab tool. Kind of feels like I'm making a paper airplane at this point, but pretty cool for a start.