How can I make professional video using an iPad?
Trade in the iPad and buy a desktop or laptop that you can edit on.  You will not produce professional results entirely on an iPad.  I am not aware of any good video editing options for iPad, certainly none of the big names have a product available.  There simply isn't enough horsepower on a tablet to perform the hard, complex operations involved in video editing in a smooth and timely manner. 

(Minor correction: There is a version of iMovie available and Pinnacle does have a video editor available as well.  These are both makers of some of the better consumer focused stuff and could be considered big names, particularly since Pinnacle was previously held by Avid for a while, but I would still consider these cumbersome and limiting.  It probably IS possible to produce a professional quality result, but you'd have to work really hard at it.) 

You could use the iPad for shooting the video and get decent results with proper usage, but you will still need a lot of other equipment to compensate for the iPad's camera short comings.  

Lighting will be super important.  You will need lots of light, placed well so that there is sufficient light for the sensor and no shadows that the camera's dynamic range can't deal with.  This is also more than just having lamps, but also the stands to position them where you need them and modifiers to adjust the way the light falls on the scene to make good, even lighting.

Sound will also be another issue.  You will want an external mic.  People have reported being able to use USB mics with the iPad Camera Connection Kit, but I couldn't find anything verifying if it would work with professional audio interfaces or a microphone more designed for video situations.  Another option (which is what you will commonly see in more professional productions) is to use a separate audio recorder, such as a Zoom h4n to record audio and sync it up in post production.  Even if you really wanted to stick with your plan to use the iPad for the editing, you could transfer the files off the SD card using the previously mentioned camera connection kit.

You will also need a stand and tripod that can hold the iPad securely.  There are numerous options available and I don't have any particular experience with any particular model, but being able to shoot stable smooth video is an absolutely critical aspect of any high quality video shoot.  If you shot is purely static, you might be able to prop it up like Jason suggested, though it also then runs the risk of slipping or more easily getting jostled, and as he points out, you won't be able to do a shot with any movement, so I'd highly recommend a tripod.

If you can handle those three things, that should allow for decent quality footage to be shot on the iPad, but you are probably looking at between $450 ($200 dirt cheap lighting, $50 tripod adapter, $50 dirt cheap tripod, $100 - $150 relatively cheap usb consumer audio mic) and $1300+ ($500 ok lighting, $250 basic pro audio recorder, $150-$200 decent video mic, $50 tripod adapter, $250-$350 ok tripod) of gear to supplement it.

I want to emphasis that the $450 is about the cheapest you could possibly go while still calling it "professional video".  You can make something that looks ok for a consumer project for less, but really pulling off professional video is unfortunately not particularly cheap even if costs have dropped like a rock in the last 10 to 15 years.  (You can now do for $15,000 what used to cost $150,000+.)

Finally, practice and experience is key.  There is more to producing professional results than the right equipment, you also need to know how to use it properly.  There is far too much to doing this to summarize in a single QA post, but pre-planning is really key.  If you know your shots and plan the video out before you shoot, you can make sure you get all the shots you need and make sure that they flow well from one to the next.  You can plan the angles to shoot from and what you want the end product to look for.  Even with hundreds of thousands of dollars of high end professional gear, the result will look like someone's home movies without planning and organization to accomplish a consistent vision for the video.