I just had to perform this exact transfer in January of this year. Unfortunately, there is no longer a free shuttle between the two terminals. (We asked the people at the information desk, they told us they stopped operating the shuttle because of "terrorism" concerns. I suspect it's actually due to cost, since people needing to transfer between the terminals are those booked on separate tickets, since the only airlines where someone can book a connection on the same ticket now operate directly out of Terminal 2. Thus, ridership on the shuttle would be much lower, so it didn't make economic sense to operate it.)
The only way to get from Terminal 1 to Terminal 2 is by private taxicab. Claim your bags at Terminal 1, then step out of the terminal. Once you're out, look for the "inter-terminal transfer" counter in the row of counters on the right side. It should be all the way to the right.
We were traveling as a group of four, with eight pieces of checked luggage and four carry-on suitcases. So, we paid for a van, which cost us 1,000 rupees. (If you're traveling in a smaller group, with fewer bags, there is also a sedan, but I don't know how much that costs.)
In addition to what we paid at the counter, we also had to pay 130 rupees twice directly to the driver, which was handed over to the toll booths for cars exiting each terminal. The total cost of the service was, therefore, 1,260 rupees. Do keep in mind that we were a family traveling with a lot of suitcases.
The ride to Terminal 2 took about 20 minutes, and we had to drive in Mumbai traffic. The two terminals are part of the same airport, but are accessed through different access roads from the highway.