Is it possible for a student in first year of Ph.D to secure funding for attending conferences? Note: I'm primarily interested in answers relevant to Computer Science (Theory), but answers in different areas in CS / totally other disciplines are equally welcome.

In most (if not all) PhD programs, incoming grad students are supposed to take relevant courses and fulfill their TA-ship duties (I'm assuming not everyone gets a RA from the 1st semester itself). During that time, they are also expected (and highly encouraged) to keep reading on their chosen research field, to have a concrete idea of where all the focus in that field is at that moment. 

In my opinion, I would consider that attending important conferences and interacting with leading researchers in their field would play a very important role in the development of a young researcher, as he/she would have the chance to get motivated by the best brains in the business! But, it is unlikely that he/she would have publishable results at such venues within such a short time, and if he/she doesn't have a fellowship/travel scholarship, it is unlikely that he'd be able to afford the registration/travel/accommodation expenses from his own stipend.

So, what are the options in front of such a student to make attending such events possible:


Do advisers cover the expenses for their incoming grad students, for
attending such talks/conferences, or is there a provision for such
funds from the department ?
How much does the answer to the above question vary between different colleges - I've heard (unconfirmed) reports that
higher-ranked institutions have more funds to burn, and as such
students in such departments can afford to attend talks without
publishing in them (at least for the first 2 semesters) ?
Are there specific scholarships/fellowships that exist to primarily cater to conference related expenses for students? If so,
it would be great to get some leads on where to look, and what are
the primary qualifications (>90% of fellowships in US require the
applicant to be an US citizen, making it extremely difficult for
international students to get one!) ?
As Willie Wong says, it depends on your school and your advisor.  As an obvious general rule, departments and advisors with more research funding are more willing to spend it.  (As a reference point, my department does not offer such funding, because individual faculty generally have enough money to support their students' travel.)

A significant number of CS theory conferences have external support for student travel; see, for example, SODA 2012 and STOC 2012.  These grants usually require a letter of support from your advisor, so you at least need an advisor.  (In many PhD programs, including mine, PhD students do not necessarily have formal advisors for the first year; students are admitted to the PhD program, not to any particular research group.)