JSON.serialize() can be used to convert sObject to JSON String in Salesforce using Apex.

JSON.deserialize() can be used to convert JSON String to sObject in Salesforce using Apex.

Sample Code:

Contact con = new Contact(
	FirstName = 'First', 
	LastName = 'Last', 
	Phone = '9999999999', 
	Email = '[email protected]'
);
/* Code to convert Contact to JSON string */
String strJSON = JSON.serialize(
	con
);
System.debug(
	'JSON String is ' + 
	strJSON
);
/* Code to convert JSON string to Contact */
Contact con1 = ( Contact ) JSON.deserialize(
	strJSON, Contact.Class
);
System.debug(
	'Contact is ' + 
	con1
);

Output: