At first you should get the UPC (Unique Porting Code). You can get it by sending SMS to 1900.
The format of the SMS is as follows:
PORT to 1900
After it you will receive your UPC from 1901 giving 8 digit alpha-numeric Unique Porting Code (UPC) and UPC expiry date in MM/DD/YYYY format by a SMS on your mobile phone.
After it you should visit to your nearest airtel outlet / showroom. There you will have to fill MNP form. MNP form means 'Mobile Number Porting'. In this MNP form you will have to fill your Current Mobile Number, Current Operator name, UPC code.
You will have to submit your Address & Id proof documents, self-attested photo and last bill copy of postpaid connection (if applicable) along-with filled MNP form and Customer Agreement Form.
After it you should buy the airtel MNP SIM card from airtel outlet / showroom. You should learn it very well that SIM charges, talktime value and porting charge are non-refundable in the event of cancellation / rejection of port-in request.
When you complete this process, the airtel will send an SMS on your old/existing operator's SIM (existing connection) intimating about the porting date and time. It will take about 2-hour 'no service period' which will begin after the porting time as given above. The 'no service period' will be between 12 midnight to 5 am during which your mobile service will not be active on any SIM.
After the 'no service period', you can replace your existing operator's SIM card with the new airtel SIM card in your handset.
I think now you will get the airtel services on your mobile phone.