The time to follow up varies depending on the stage of the application you're in. If you've only made an initial application and haven't had any contact from the company, wait 1-2 weeks before following up. You can also check if the advertisement gives any timeframe on when you can expect to hear from them. If you've already had an interview, it's good to follow up immediately afterward as an acknowledgment. After that, wait another 1-2 weeks if you haven't heard an update from them - unless you were given a specific timeframe.
Whatever stage of the application you're in, express your enthusiasm for the role and highlight a few of your strengths. If you've just made the initial application, you might say that you want to verify it got to the right person. After an interview, thank the person and give examples of your continued interest in the position. If you haven't heard back within the expected time after an interview, politely ask when they might make a decision.
Be patient with the process and remain courteous while following up. One follow up demonstrates initiative and sincere interest in a position. On the other hand, multiple emails demanding to know the status of your application creates a negative impression. HR offices and hiring managers are busy; they may be screening through hundreds of applicants. There may be a lot of paperwork involved in the process, so be understanding.
Even if you follow up, you can't always expect a reply, especially in the early stages. If the job ad says “only short-listed candidates will be contacted”, they won't respond to your follow up unless they short-list you. However, if they're deciding which candidates to short-list, your enthusiastic message may make you stand out. If you're inquiring after an interview, you should get a response as both sides have put in more effort.
When to follow up
Express enthusiasm and emphasise how you're suited for the role
Be patient with the process and don't send too many emails
What you can expect