The simplest and most direct method is nohup java -jar jenkins.war &. "nohup" means "no hangup", which is vintage terminology for not ending a session when the terminal disconnects. "&" just starts the process in the background, similar to what would happen if you press CTRL+Z (and then type bg 1) while the process is running in the foreground.

WARNING: nohup, by default, sends output of the process to a text file. If you are not careful, that file can become dangerously large in some cases. Treat it like any other ever-growing log file.