I bought 2 packs of black self-tapping screws - one pack of about 2-3cm long screws & another pack of longer ones (5-6cm).
I then used my Dremel to modify the tabs on the splitter, smoothing them flat & also trimmed down the central struts. I wanted the splitter to curve up a bit in the middle to follow the line of the bumper, but you're best off trimming a little bit off at a time & then trial-fitting until you decide on how you want it to sit.
I pre-drilled a hole in each tab (about 20 I think), then positioned the splitter on the car using wide masking tape, making sure it was evenly positioned on each side (where the wheel arch begins, etc)... then it was just a case of screwing through my guide holes into the bottom edge of the bumper using the smaller screws.
In the pic, you'll see how the central section is hanging down a bit - I hadn't added the longer screws which I have on there now. The splitter struts are kind of V-shaped, so as I screwed it in, it pulled tight.
My coilovers have settled in now & so the car's a fraction lower. That, combined with the crappy UK roads/camber/ramps/etc has meant I've scraped the splitter a few times. It seems the screws work well as they just pull out when you catch it & you can just put new screws in.
I like how it finishes off the bumper & looks OEM, but still adds an agressive edge to the car's appearance.