Is it possible for a student in first year of Ph.D to secure funding for attending conferences?
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.)