online trading bot

First, you should note that some online games forbid bots, as they can give certain players unfair advantages. The MTGO Terms of Service do not seem to say anything about this, though they do put restrictions on anything that might negatively impact the service. They have also said that there is a possibility they will add an API in the future, so they don't seem to be against the idea of automation, but are not supporting it at the moment. Tread carefully here, but it looks like it should be OK to write a bot as long as it is not harmful or abusive. This is not legal advice, and it would be a good idea to ask the folks who run MTGO for permission. edit since I wrote this, it has been pointed out that there are lots of bots already, so there should be no problems writing bots.

Assuming that it is not forbidden by the terms of service, but they do not have an API, you will have to find a way to detect what's going on, and control the game automatically. There's a pretty good series of articles on writing poker bots (archived copy), which has some good information on how to inject a DLL into an application, scrape the screen, and control the application. That might provide you with a starting point for doing this sort of thing.

You might also want to look for tools that other people have already written for doing this. It looks like there are several existing MTGO bots, but they all seem a bit sketchy (there have been some reports of them stealing passwords), so be careful there.

Edit

Since this answer still seems to be getting upvotes, I should probably update it with some more useful information. Since writing this, I have found a great UI automation system called Sikuli. It allows you to write programs in Python that automate a GUI. It includes image recognition features which make it very easy to recognize buttons, cards, and other UI elements; you just take a screenshot, crop it down to include just the thing you're interested in, and do fuzzy image matching (so that changing backgrounds and the like doesn't cause the match to fail). It even includes a custom IDE that allows you to embed those screenshots directly in your source code, so you can see exactly what the code is looking for. Here's an example from the documentation (apologies for the code formatting, doing images inline in code is not easy given StackOverflow's restricted subset of HTML):

def resizeApp(app, dx, dy):                      
    switchApp(app)                                
    corner = find(Pattern().targetOffset(3,14)) 
                                                  
    drop_point = corner.getTarget().offset(dx, dy)
    dragDrop(corner, drop_point)                  
                                                  
resizeApp("Safari", 50, 50)                      


This is much easier to get started with than the techniques mentioned in the article linked above, of injecting a DLL into the process you are debugging. Sikuli runs entirely at the UI level, so you never have to modify the program you are automating or worry about changes to the internals breaking your script.

One thing it is a bit poor at is handling text; it has OCR features, but they aren't all that good. If the text is selectable, however, you can select the text, copy it, and then look directly at the clipboard.

If I were to write a bot to automate something without a good API or text-based interface, Sikuli is probably the first tool I would reach for.

This answer is constructed from my comments.

What you are trying to do is hard, any way you try and do it.
Arguably the easiest way to do it is to totally mimic the user. So the application presses buttons, moves the mouse etc. The downside with this is that it is dependant on being able to recognise the screen.
This is easier if you can alter the games files as you can then just skin ( changing the image (texture)) the required cards to a single unique colour.
The major down side is you have to have the game as the top level window or have the game running in a virtual machine. Neither of which is ideal.

Another method is to read the processes memory. You may be able to find a list of memory locations, which would make things simpler, otherwise it involves a lot of hardwork, a debugger to deduce the memory addresses. It also helps (a lot) to be able to understand assembly.

The third method is to intercept the packets, and alter them. This is easier that the method above as it (at least for me) is easier to reverse engine the protocol as you have less information to deal with. It is just a matter of setting up a packet sniffer and preforming a action with one variable different (for example, the card) and comparing the differences.

The thing you need to check are that you are not breaking the EULA. I don't know how the game works, but most of the games I have come across have a EULA that prohibits (i.e. You get banned) doing any of the things I have mentioned.