I absolutely absolutely LOVE my EQ7 software. I got it in I think 2010 or 2011, and started designing right away.
Kathy gives a good overview of it; I will add that "drawing your own" is a little harder if you want to be able to draw freehand shapes. I have managed it, but usually with some tweaking. For straight lines or geometric shapes, it is wonderful, but it is NOT like drawing in, say, Paint (the program), more like adding lines/shapes/drawings to a document (as far as the interface, ability to freely draw, etc.). Or, there may be ways, but I haven't found them yet.
What I mainly use it for is fabric play (I often use just plain colors or default fabrics to get "a vague idea" vs. true image of what it will be like), testing out different colorings of things. Then I rely on it for calculating yardage, and Kathy's tips are good there.
Example, I drew a Sunbonnet Sue quilt for my sister. I selected the basic Sunbonnet Sue block from the block library in EQ7, selected an Overall Sam block to go with it, selected a quilt layout from the layout library to get a basic horizontal layout with sashing between the rows. I selected what size finished block I wanted each block, and what size sashing, as well as how many blocks across and up & down, then played with those values until the quilt overall size was what she wanted. The software makes this very easy, simply type in the different numbers in teh correct place and it calculates the total size automatically, showing you at the top of the screen how big the overall quilt is, and when you add borders, it shows you with each individual border the overall size up to that border and up to the whole quilt (in 2 different places).
With this quilt, then for the yardage estimates I did one coloring showing all hats one color, all arms one color, all bodies one color, etc. so she would know (she was making a scrappy one) how much total yardage for each piece, in whatever colors she wanted, and another coloring in scrappy style showing her some suggested ways to do that. Then do the print preview as Kathy described. I also was able to print the templates and save as a PDF file, email to my sister, and she was able to put that PDF file into her Sixxix cutter (I think is the one she has) and cut the pieces that way, but that's only a bonus if you have a cutter that will do that; otherwise though you can print the templates for applique, as well as foundation templates for paper piecing, for any block in the program, whether one you design or one from the library.
Each block can print rotary cutting instructions (it calculates the seam allowance, and you select whether to print at the nearest 1/8th inch or nearest 1/16th inch), templates, or foundation, depending on the style block. If a block can be done multiple ways, you can print all the types. ON fabric yardage you select how wide the fabric is, as well, when it calculates the yardage needed.
I rely on it completely for all my quilt math, for previewing a design/color before committing, etc. Like Kathy said, you just keep saving and click "add to sketchbook" for each different design/color you do, and you can then click through each one to see/decide what you like (so when you change it, you don't lose everything as long as you've first added to sketchbook and can easily go back to a previous version).
I think EQ Stitch was promoted as "EQ7 Lite" so does more than just embroidery, but I"m not sure, I could be wrong. EQ7 does have quilting designs, too, you can try out, print, etc. as well, so really is a full service program; I haven't used Stitch, so not sure what all it does. The tutorials in the software itself and in the book that comes with it are pretty good; it is overwhelming the first time you turn it on, but a little while of playing with it and you'll figure it out. Easiest way would be to start with one of the Quick Start projects included in the opening menu and from within one of those, play with how to change the color, layout, etc. before starting to try designing your own. Or start with a simple layout from the layout library, pick a few blocks, and place them in.
I design all my own stuff, though, very rarely do I use a pattern, and always do I use EQ7 to figure things out for any quilt I make.