A lot of people will tell you many different things about finding that "dream job". Some of the advice will seem helpful, some of it won't, but the truth is that the job hunt is different for everyone.
Whatever position it is you're looking for, even if the person giving you the advice was going for the exact same one, it's going to give you a unique experience.
Maybe the most important thing to remember – and that's exactly why it's being mentioned first – is that you have to stay positive. It's easier said than done (just ask anyone that's had to do it), but staying positive really is the best way to approach the situation. At the end of a long day spent sending application after application, it can be very easy to grow disillusioned, but just remember that, as hard as it gets, you absolutely can do it.
Secondly – and there's probably an argument to have this point first – make sure you know what you're aiming for. It might sound strange, but it's easier than you'd think to apply for a job only to realise – once they've given you an interview, of course – you don't know enough about what it is you'd be doing in that job. So always make sure that, when you're applying for a position, you know which skills and experiences would be relevant. If you have them then great, if not, it's an opportunity for you to let your potential employer know why they should hire you anyway.
Last but not least: be professional. Even if you get rejected for a job, and even if you don't hear back from some of the positions you applied for, keep your calm. If you get an email telling you that you've just missed out, reply – let them know that you're grateful for the opportunity. It might not be much, but it might be just enough to keep you in their head so that, next time a position opens up, it could be you filling the void.