Some knitters won't consider a pattern requiring a long cast on. But casting on a lot of stitches is really the same as casting on a few. You do them one at a time. But you can make the process a little easier.
The first thing I do is make little stitch markers from lightweight scrap yarn. One marker for every 50 stitches to cast on. I start with the exact number needed -- when there are none left, I just have the final (less than 50) stitches to go. It's an easy way of knowing where you are at any point without needing to count. I like to use 50 stitches between markers because a) it makes for easy arithmetic and b) I can count to 50 without losing my place or getting distracted. You can chose any number you want. For my 745 stitch cast on I made 14 stitch markers.
Type of Cast On
There are books written on various ways to cast on. For shawls, I like one that's somewhat stretchy and looks neat (many stretchy cast ons tend to be sloppy and loopy). One of my favorites is the Old Norwegian cast on (in part because it's the one I learned as a young girl). Typically in a long tail cast on you have to estimate how much yarn you'll need before starting.....not easy to do with lots of stitches. Too long a tail is wasteful (and prone to tangling). Too short a tail....and you'll run out before you're done (argh!). To eliminate that problem, I use two separate yarns -- either from separate balls or opposite ends of the same ball. In this case, I used two separate balls -- one in the main color (solid) and one in the contrasting color (variegated). The yarn over your index finger will be the yarn forming the stitch on the needle. The yarn in the "slingshot" position will be along the edge.
I don't know how long it took to cast on the 745 stitches -- I worked at it over the course of a few hours -- 50 here, 50 there, fitting it in around other tasks. Not hard at all.