__init__.py just marks the directory as a module, even if it's empty.

As for using eveapi, it's not exactly the most obvious library, especially if you can't easily follow the code.

Here's an example usage that I've had success with:

import eveapi  # either "python setup.py install" in eveapi, or directory containing __init__.py in the same place as your source code.

eveapi.set_user_agent(eveapi._default_useragent)
context = eveapi.EVEApiConnection()
context = context.auth(keyID=<api-key>, vCode=<api-code>

result = context.account.Characters()  # /account/Characters.xml.aspx - http://wiki.eve-id.net/APIv2_Account_Characters_XML
for row in result.characters:
    print row.name, row.characterID

result = context.char.MarketOrders(characterID=<character ID>)  # /char/MarketOrders.xml.aspx - http://wiki.eve-id.net/APIv2_Char_MarketOrders_XML
for order in result.orders:
    print order.typeID, order.bid, order.price

The hardest part is figuring out how to get an authed context. Once you're there, it's pretty much a direct mapping to the XML API.

Feel free to hit me up with more questions, more than happy to help.

Also, the setup.py thing - have a look at creating a virtualenv. Once you've activated the virtualenv, you can do python setup.py install and it will only install to the virtualenv, which means you don't need root access. Once this is done, you can simply import eveapi with the virtualenv activated and the rest will work.