Different sites will have different ways to prove qualifications. Some just require that you state that you qualify, others want a copy of transcript, others want copy of student id.
Microsoft's policy is that the reseller is supposed to ask for student id. but again, that will vary, simply because some resellers will ignore MS policy. And some resellers only randomly ask for proof.
Another type of discount out there for software is OEM versions. Theyre intended for sale with computer system, but some companies say "with computer hardware". So, some resellers will include some cheap piece of hardware (ie: a mouse, a cpu fan, etc). Again, mileage will vary.
Of course, when searching for such retailers, be aware that there are many scam sites and fake sites out there that searches will pull up, and many selling counterfeit copies that searches will pull up. If it says that you'll be able to download the software, RUN THE OTHER WAY!
As always, look for key things, such as professional site, how long they've been around, etc. Newegg.com is one site that sells lots of academic and oem software, and theyre reputable. right now they dont have much in the way of academic, didnt check their oem stock.
If youre willing to go with something else besides Dreamweaver, then there are some free options out there, such as AceHTML http://www.download.com/AceHTML-Freeware/3000-2048_4-10524593.html?tag=lst-0-8