Once I had the plot and the characters mapped out, I started to the think about writing it. I wrote a very rough version of the first half, up to the point that Ellie leaves, and then stopped. I went back over, editing the dialogue a lot in order to make it seem as natural as possible - I wanted it to feel believable.
I then wrote Matt's section separately. For this I had the idea of a waiter, who was very confusing. One minute he was very deep and meaningful, and the next he didn't care at all (In my head, this was funny. It didn't turn out so well on the page). I wrote that out, went through and edited that, and then put it below the rest of the script. I then started on Ellie's section, for which I wanted her to be mostly on her own. I decided that it would be fun for her to have to look after a dog, and I wrote in an old woman who would come past, leave her dog with Ellie, and then cross through into Matt's section. I was happy with Ellie's section.
I then put it all together. This wasn't quite the first draft though (They were still called Brett and Erin at this point!). That came just a tad later.