I suggest to use Miller and Doyle model to evaluate the effectiveness of e-government system! also the model provided by DeLone and McLean is very useful and widely cited in this context.
The most cited goal of e-government is to provide a better public service delivery to citizens. Therefore, in my point of view, to measure the effectiveness of e-government is to measure citizen's attitude on e-government. For example; whether most of the citizens use the e-government for obtaining services or not. Since your question is about theories, I would suggest taking one of the following theories; - Technology Acceptance Model, Theory of Planned Behaviour, Unified Theory of Acceptance and Use of Technology, or Theory of Reasoned Action. These theories are aimed to measure the Demand-side of e-government.
If you want to measure the supply side, you can take from DeLone & McLeans model.
As for the practical approach, the PDF sent by Elahe Meydani is a good source.