Hi
My first question to you is why do you need to learn the nature of the day to day role? Are you a new BA? Are you a student writing an assignment? Are you some other person on a project team trying to work with a BA? This will help us answer your question better.
Presuming you are a new BA…
Adrian is right, it's just too large a topic for a discussion thread to give thorough details of projects we have worked on. Additionally many of the projects are commercially sensitive and so we can't share much of the content in a public forum.
I would go to the IIBA website and download the BABOK as a starting point. It is a large document with plenty of information. It is designed to help you work your way through the process. Beyond that I would look to requirements planning to help you understand what you need to do.
You specifically asked about some of the start-up tasks. I have provided links to my blog on topics where I have written about them and Tyner Blain where I have not covered the area. Don't stop there. You can search out more information. In particular look to your corporate intranet or templates library for documents you can use to guide you through the process.
a) The nature of your project - project scope management; what is the product or service you are trying to produce and what work is going to be done to get there. This is quite a wide ranging topic. Start your search here and also read on the topic of requirements management and scope management.
b) Your elicitation techniques pertaining to your project - Donald Firesmith writes an excellent article on the topic of elicitation of and documenting requirements. You can get to the article from here.
c ) Softwares/modelling tools used - Use Cases and Process Maps are popular tools for documenting requirements, and there are plenty of others. Firesmith's article probably tackles this sufficiently, but check the Modern Analyst thread on requirements also. Start a thread if your answers are not already there. Finally I have a soft spot for a workshop technique called Method H which is both simple and useful. It even comes with a cheap ($35) software tool. A note – the tools and methods you employ may depend on the type of project process you are following.
d) The stakeholder's you dealt with and what were your queries for them - Stakeholder management is a key to successful projects. The first step is identifying them, then talking to them and understanding their needs. You shouldn't just do what they all ask for, but instead balance their needs with those of the project sponsor. Fulfil their expectations by managing them.