With acrylic yarn, blocking doesn’t do very much. It may help even out your stitches a little bit, but unlike wool or animal fiber yarns, acrylic doesn’t really “need” to be blocked. However, it won’t hurt, and is basically just like giving the shawl a wash before it is worn.
First, you’ll want to get the shawl wet in a gentle bath of warm water, and maybe some mild soap if you want. Let it soak for 20 min or so. Drain the water, and press the shawl against the bottom of the bath. Don’t wring it out. Lift the shawl into a towel, and press more water out of it. I often fold up an finished project in a couple of towels then walk on it to press the water out. After it’s mostly dry, spread it out for blocking.
You could block on a piece of cardboard. I’ve blocked on a spare bed, on a carpeted floor with a towel under it, on a card table with a towel under it, and even on the top of my washing machine (with a towel under it). I’ve heard that cork bulletin boards (laid flat) also work well.
Depending on how the shawl looks pre-blocking, you may not need to place pins at all. If it mostly looks how you want it to look when it’s done, just lay it out nicely in the shape that you want the final to take. If you do decide to use pins, place them frequently around the edge of the shawl. If there’s a long straight edge (i can’t tell from the photos), you may want to consider using this method. The general rule of thumb for pin placement is to put them around the edges so as to make the final product the shape that you want it to be.
If you’re not already a member of ravelry , you should definitely join. There’s almost 1,000,000 members world-wide, all crocheters, knitters, spinners, weavers, etc. There forums would be another good place to ask this question, you’ll get responses from much more experienced fiber-artists than myself.
Again, I think in this case blocking is probably optional, since you’re working with acrylic yarn. If you like the way it looks now, just let it be! Or if it needs a wash, give it a gentle bath and lay it flat to dry.
Good luck, and let me know what you do! Also, if you join ravelry my username is hannahsug. :)