The law making process is initiated in two levels. In central level the parliament and in State level legislative assemblies and councils takes hand on making laws. The law making process mainly goes through 4 different rounds. 
Round 1
First, there should be a need for law or for an existing legislation to get amended. Anyone who are a citizen of the country can raise the need for a law.
Round 2
The ministry who have the concern will propose the law which is called as a "Bill". The bill is handed over to the ministers. The public is also given the right to express their feedbacks. After the feedbacks recived by the public are added by the ministry of law and is presented to the cabinet for approval.

Round 3
After getting the  approval from the cabinet the bill is passed on to the parliament. The parliament is considered as the central legislative of law making. Every bill is underwent a number of 3 readings in the parliament.
First Reading, 
 The law is introduced in the parliament which might be opposed and put into vote. The Presiding Officer ie. Speaker of Lok Sabha or Chairman of Rajya Sabha will sent the bill to a standing committie for asking public opinions and suggestions on the bill.
Second Reading,
The bill is considered again which might get approved or rejected. The bill is scrutinized and discussed here. 
Third Reading,
The house votes on the bill and the bill is passed at the third reading. Like ways the next house also under goes the same rounds.
Round 4
The bill thus got passed from both the houses is send for the approval of the President Of India. The President can ask clarity or even return to the parliament for reconsideration. This step can be taken by the president only once. 

Round 5
The President Of India approves the bill and is approved as an Act. This is later ap[proved and amanded as a bill.