I receive many SMS regularly offering Instant loans. Though I haven't taken such a loan before, I have an idea of how they work.
When you go the links they share, you are required to fill a short form which takes all your important details like address proof, identity proof, PAN card number and Aadhar. The PAN card number basically gives them your Credit report. This report is present for each individual which a PAN card and contains all the history of your previous loans. If you use a Credit card a lot and haven't defaulted ever, your credit card score will be superb. If you don't use a Credit card or haven't taken a loan before, then also your Credit score will be good.
Based on your credit score and your income details, these companies offer your loans. Since they are the ones giving you money, it is more a matter of THEM trusting YOU. However, since you are sharing sensitive information, you must carry out a basic check who these companies are and their trustworthiness. I have found out that many of these companies are actually financed by big banks or finance companies which gives them their trustworthiness.
If you are doubtful, you always have your own bank to revert to in case of loans but they might not be as fast as these companies.
If you have a salary account, then you can avail such instant loan facility from them. For instance, I have a Citibank account and I receive regular mailers informing me that I am approved for a loan of an X amount. Since they already know how much I earn and my spending habits, they don't need any details and can process the loan immediately. Contact your bank for more details.