Because there is no player on the other end of Instant Selling to obtain the Pokemon, Instant Selling is synonymous to deleting a Pokemon for money. Pokemon that have been Instant Sold are gone forever and unretrievable.
The option to Instant Sell can be found in the bottom category, "Money/Shops," of the right column.
Instant Selling Pokemon grants a set amount of Platinum coins in proportion to the level of the sold Pokemon (with variance.) It is usually less than what many players would be willing to pay for, meaning your net profit goes down.
A level 1 Pokemon will sell for approximately $350.
A level 10 Pokemon will sell for approximately $1000.
A level 100 Pokemon will sell for approximately $20,000.
Besides for levels, there is another factor that can affect its sale price. If it is an ungendered pokemon, it Instant Sells for more Platinum coins.
The amount of that pokemon in game and whether or not it is legendary seems to not affect the sale price.