The best tip I was given was to ALWAYS follow up applications. If you think you're harassing them, from their point of view it shows you're really interested in the job. The worst you'll get is a no, you haven't been selected. But even then, it'll be clear.
You should never just apply online and then forget about it, depending on the job sector (restaurants and fast food tend to reply way faster cause they're always short on staff) write down a way to contact them and call around a week after applying if you haven't had news about your application. Sometimes applications get lost, or they forgot to reply.
I've changed jobs a lot in the last five years (minimum a month, maximum a year) and had to apply online a LOT so here are some tips:
- Write down on a paper or excel sheet all the info about the job, INCLUDING the address or a phone number AND the date you applied
- Always include a motivation letter if the option is given to you
- If you don't have an answer (positive or negative) about 1-2 weeks after applying, contact them to ask about it. Two weeks is a lot outside of summer vacation (applying in August in France is hell because half of employers are on vacation and the other half isn't qualified to interview you)
- If the previous step didn't work (and if it's possible), show up in person.
- Know when to give up insisting, after 3-4 weeks without any kind of reply, move on. Consider your application rejected.
But yeah, the best is to go there yourself and physically hand out your application, or to do some digging and find out when the manager is working so you can give them directly.