it really depends on what you are doing to give you a solid answer.

service broker calls run asynchronously; (sending mail via sp_send_dbmail is one common example) so you'd need to add a service broker that can execute a specific command or set of commands.

you could start with a search for "sql server service broker example", and start from there;

do you really need multiple async processes , or just to have one process do a bunch of stuff async so you can return control to your proc immediately??