There is no single or fixed location or exchange where debt market participants transact. Also very sadly small investors have no role to play. Which means as a lay investor you can invest in equities (far more difficult to understand) but cannot invest in debt markets (easier to understand).

Dealings are done over phone, and confirmed by fax, email, etc. It is a virtual market (on the net). All the Indian stock exchanges (Bse, nse, otcei) have a separate debt market segment. Debt markets deal with Government securities market and Bond markets.

Sadly in this market the only issuer is the government of India. The government has a vested interest in keeping the interest rates low, and we cannot do anything about it!