//load the process by ID 
var process = PublicAPI.Processes.WorkflowProcess.Load(3);
//process instance name 
var instanceName = "Process instance name";
//disable the error message (yes or no) 
var offException = false;

//create an anonimous object for conveying the context to process 
//names of the context variables which can be found in the designer, "Processes" section, "Context" tab 
object objectContext = new {CeloeChislo = 29, Stroka = "String via object"};

//CeloeChsilo и Stroka are the context variable names 
//These names must coincide with the context variables names, otherwise an exception is invoked 

//start the process
PublicAPI.Processes.WorkflowInstance.StartProcess(process, instanceName, objectContext, offException);

//WARNING!! This method will return exception, if the names in objectContext will not coincide with the context variables names 
//and the offException parameter takes the false value. If offException takes the true value, the exception will not be returned