The other answer is incorrect.
See the ERC721 Standard for exactly how to do this. If a token contract properly implements the ERC721 Standard and the ERC721Metadata extension, it will always implement the function
function tokenURI(uint256 _tokenId) external view returns (string);
which will return a URI pointing to that token's metadata. It may be in JSON format, and if it is, see the standard for the structure of the ERC721 Metadata JSON Schema.
Any methods which retrieve token metadata other than this are not part of the ERC721 Standard. This isn't to say that they break any rules set out by the standard, but the only guaranteed way to get ERC721 token Metadata on a properly implemented ERC721 contract is through the method mentioned above.