When we have to fill forms for PSU's( in our final year or after gate exam ) and how we can apply for different PSU's?

All the PSU's do not take admission through GATE. Some of them take through GATE. The PSU  will advertise the vacancies and will let you know if they will be selecting through GATE. IN any case you will have to write the GATE exam. In order to get placed early, it is advisable that you give the GATE exam in your final year and keep track of the announcements that are made  for vacancies by the PSUs.