I always do it myself. It doesn't take much time to hunt and peck for discounts (
Mouse Savers,
WDW Info [here], and
All Ears keep everything very up to date). A quick glance at one web page and I'm off!
I do it via phone. It generally only takes one phone call. Maybe a second or third to get ADRs if I book before my window or a code comes out after I book. No phone call is very long. Whose cell phone doesn't offer free long distance? Plus, we now have unlimited long distance on our land line. DH also has VoIP for work which also includes free long distance.
I prefer phone so I can ask questions (Is there any discounts on this room during my visit?) since sometimes things like manager specials pop up and those are not advertised anywhere! Also, sometimes you miss the pin code they send out. Disney will not offer discounts, you must ask. Another reason I like the phone is that when you book via phone you get more lenient cancelation procedures than if you book via internet.
I never use a TA since I'm dependent on them to make changes and they have to help other customers too. Not to mention, they have lives of their own--they might be on vacation when something comes up and the TA helping them will most likely help their customers first. Sometimes there are limited rooms and if they don't get to me right away, I might miss something. I also find that cutting out the middle man just saves time and I never have to worry if they did it or got it right, referring to ADRs here. I have nothing against (good) TAs, they're just not for me in regards to booking a Disney vacation!