We applied to ESF schools last June using their Corporate Surety Scheme. See their website under "Admissions Criteria"; at the bottom of the page.
We did all of this prior to coming to Hong Kong. It took me a bit of research to figure it all out, but it was quite easy in the end. We just filled out the application forms while we were still at home, sending it to my husband's new employer in HK, which they then submitted to ESF with one month's tuition. While this money is not refunded it is a small price to pay for getting your kids into school prior to a move. You can also apply earlier, but it cost progressively more. On the application they ask where you plan to live or what schools you would like to attend, if I remember correctly. We stated we would prefer to live in a particular area, Pokfulam since my husband works in Sheung Wan, but would live in a different area if our kids were accepted into schools in a different area.
In the end it worked out quite well as all 5 of our kids were accepted. The 3 younger ones at Kennedy school and the older 2 at Island School. We've been really happy with both of these schools and I suspect that we would have been with any of the ESF schools. I'm just relieved that I only have 2 schools to deal with as I had feared that the kids would be split up and going in all directions to various schools!
The only testing they had to do was a quick interview or two. When we arrived in Hong Kong in mid August each child had an interview and English proficiency test. While that was a bit rushed, and my younger kids didn't start school until the second week due to scheduling of these tests, it all has worked out surprisingly well and my kids are quite happy.
Hope this helps.