You are not going to be able to get the sound you want from your stock acoustic guitar.
There are two particularly important elements that contribute to the sound of a sitar. One is the unique design of the bridge, which creates a buzzing sound, and the other is the presence of many additional sympathetic strings. In order to get this sound from an acoustic guitar, you would have to dramatically rebuild it from inside out. This would not be practical.
There are professional Indian musicians who have done this with a guitar. Here are some pictures I found in a Google search.
All those extra tuning pegs are for the extra strings that have been added, and the guitar had to be massively reinforced to handle the tension of all those extra strings. Also, these examples are usually played with a bottleneck slide, not fingered like a conventional sitar or guitar.
It would be much more practical for you to spend US $700 or so on an electric sitar guitar, such as the Italia Modena Sitar model. Notice that it has 12 extra sympathetic strings that are not connected to the neck of the guitar (the instrument has 18 strings in all), and that it has the special buzzing sitar-like bridge under the main six strings.