For example, Government bonds are often sold at auction with bidders giving the best price. This price could be higher, equal to or lower than face value.
The price is determined by a number of different things such as credit worthiness of the issuing institution (higher credit rating results in higher prices), investor preference (coupon size, maturity etc). Ultimately the return (is the Yield To Maturity) will be equal to equivalent investments out there and the price will adjust to make this happen. For example if government bonds generally pay around 3% YTM and a 4% coupon bond is issued, its price will be higher than face value such that the YTM will be around 3%
If your question is about price at issuance, it is always face value right before it hits the market so at face value is the answer