How do I get my website noticed through press releases?

I agree with Humberto just firing off a press release isn't likely to get you much in the way of valuable press mentions.

This is a really good guide on DIY PR:

http://okdork.com/2014/08/12/how-to-do-pr-for-your-startup-without-spending-any-money/

Your press release should mention "Interactive press release" when emailed to the press. There should be a live link enabling journalist to download photos, videos and links to your content. You should have a boilerplate (i.e a mini-resume) about your company at the bottom of the page. The most important part is your banner title. Make sure it's catchy and try to announce something worth printing that will truly engage the audience of the media you are soliciting. Ask yourself: Is this relevant to the audience they are reaching? Try calling first to request the permission to email and confirm the email address. Getting that permission is key, it will increase your chances of getting coverage.

I own a digital agency called Noticed, we haven't recommended press releases to our clients for more than 4 years.

Press releases are for dinosaurs, its probably the worst way to market your business.

A quicker growth strategy would be PPC, Social Media Marketing, Email Marketing etc.

Why are you concentrating on press releases?

Unfortunately, press releases just aren't what they used to be. If you're looking for legitimate journalists to notice you and your website, you're probably better off trying other means. Look into what is called "Social PR."

Basically, one tactic is to engage with journalists on their own turf. Twitter is a great place to find and chat with journalists. But be careful; you don't want to "close on the first date" if you know what I mean. Don't try to pitch them a story right away. Build up rapport over time and then go in for the hook.

So personally, I would invest time and money into that, rather than churning out press releases that don't really get seen anymore.

I disagree with most of the previous answers. We use a proprietary PR system along with the Vocus/Cision Dashboard for distributing our news.We have been doing it effectively since 2005. In a recent "Newsblast" for a company with No brand recognition we achieved the following results in the first ten days:
-182,000 views of the release
-4500 full page reads
-1257 web visits (to a site that never existed prior to release
-200 RSS media Links
-2 Organic Media Stories (1 Broadcast)
-and 40% funding
We eventually did a follow-up release and our total Impressions for the campaign were over 250,000.
PR is treated by my firm as an excellent way to get some momentum built without a huge expense...quickly! PPC was used effectively alongside of the PR but performed with less efficiency. Also, I would much rather have a click referral from a newsblast (release) because the individual clicking has so much more info than you can get in a 3 line PPC ad? Lastly we build all of our PR Programs in 3 Segments.
-News Distribution
-Social Media Augmentation
-Separate Organic Pitches to targeted Media
In this particular example we raised 100% of our crowdfunding goal in 6 weeks with 92 Donors but we only had about 3 Organic Media Stories. You can see and read more about our Quick2Brand "Newsblast at: http://consultaro.com/quick2brand/ or see Michael Walsh's article "Is the Press Release Dead? No it is your amplification engine" https://www.linkedin.com/pulse/press-release-dead-nope-its-michael?trk=object-title
We are frankly tired of those that dismiss the distribution of PR out of hand without the knowledge or the experience of our system. (We partner frequently with consultants and agencies that do not have this expertise and they love us)