When I worked this pattern, I first made all the spirals, then squared them, then put the strips together, finished those, put those together, the finished the blanket.  This worked best for me and is how I've presented the pattern.

Please give me any feedback you have--I'm not much for writting pattens and if I've made anything confusing, I'd love to know so I can clarify it!

Finished Size:
My blanket came out to about 50 inches by about 77 inches, with a good about of give to it.  Perfect for cuddling up with on the couch!

Hook:
US G/6/4mm
 
Yarn:
4 colors (referred to as A, B, C, D.)  You can use a rain bow, four shades of the same color, or two of each...the posibilities are endless!  However, you should *always* start with the same color when doing your spiral. I used about 2 and a half skeins of Caron Simply Soft ( http://www.caron.com/color_cards/cc_simplysoft.html ) of each color, but I also wasted a lot of yarn on some screwups.  It may only need 2 skeins of each color.
 
Stitches:
ss - slip stitch
ch - chain
sc - single crochet
hdc - half double crochet
dc - double crochet
tc - treble crochet
rsc - reverse single crochet ( http://crochet.about.com/library/weekly/aa112997.htm )

 
Spiral:
Please note: this must be worked with four seperate skeins of yarn. Between each color, drop the previous color, and hold the loop open with a stitch marker (or just be very careful!) When you pick up the next color, you will be working into the 'back' of the previous color.  IE: when you pick up color A, you're working into color D.  When you pick up color B, you're working into color A.  You can see this in action here: http://smoothfoxlover.blogspot.com/2011/03/smoothfoxs-four-color-spiral-blanket.html .  (This is a different pattern, but a similar idea.)
 
Start with a magic circle.  (Tutorial: http://www.crochetme.com/forums/t/28917.aspx )  You can do a standard chain 4 circle to start, but using hte magic circle gives you a more solid spiral.  BE CAREFUL.  If you cut the 'tail' of the yarn too close, the center will collapse.  Leave this tail long and weave it into your spiral.
 
Row 1: In the magic circle, 1 ch 1 sc 1 hdc 2dc with each color, begining with Color A.  Tighten the magic circle until it is secure. (4 in each color)
Row  2: 1 dc in sc, 2 dc in hdc, 1 dc in dc with each color into the stitches worked in the previous color, begining with Color A.  This will secure the yarn and begin to grow the spiral (4 in each color)
Row 3: 2dc 1dc 2dc 1dc in the next 4 dc with each color (6 in each color)
Row 4: [2dc 1dc in the next 2 dc] x 3 with each color (9 in each color)
Row 5: [2dc 1dc 1dc in the next 3 dc] x 3  with each color (12 in each color)
Row 6: [2dc 1dc 1dc in the next 3 dc] x 4 in the next 4 dc with each color (16 in each color)
Row 7 (finish): 2dc 3hdc 2sc 2 ss in the next 4 dc with each color (9 in each color)

Create 32.

"Squaring" the spirals:
Do 8 in each of your spiral colors.  You could also use a contrasting color, black, white, etc if you wanted to make the spiral stand out.

Row 1: Start at the end of a color.  This will be your corner.  Attach yarn, ch 3, 2 tc in the same stitch. On the 'side' 3dc 3hdc 4sc 3hdc 3dc (one stitch in each stitch.)  In the corners (at the end of the colors), 2tc 1ch 2tc.  To finish the last corner, one tc, and slipstitch to the chain 3.
Row 2: Attach yarn, ch 3, 2 tc in the same stitch.  On the side 3tc 5dc 3hdc 5dc 3tc (one stitch in each stitch.)  In the corner, 2tc 1ch 2tc.  To finish the last corner, one tc, and slipstitch to the chain 3.
Row 3: dc around, with 3dc, ch1, 3dc in each corner.

In the back loops, ss the squared spirals together in long strips of 8. When you do this, be careful you make the spirals all face the same direction. I did mine such that each row is a quarter turn from the previous row. It is up to you, but random looks sloppy.

Finishing the strips:
Row 1: Using the same color as the finishing rounds, dc in each stitch on the long side with two tc on each side of every join. Sc in each stitch on the short sides.  For the corners, (3dc ch 1 3sc) or (3sc ch 1 3 dc).
Row 2: dc all around
 
In the back loops, ss strips together.  I ordered them in the order of the yarn in the spiral.  Color A on the left, then B, then C, then D.

Blanket edge:
Row 1: dc in each stitch with two tc on each side of every join. Change colors as desired (IE: I used Color A to stitches in to Color A, then picked up Color B for the Color B sections.)
Row 2: rsc in each sttich around changing colors as in Row 1.  In the corners, only do one rsc. This will give them a nice rounded edge.