There are, I believe, two ways to handle this undertaking. The straightforward method and the complicated way!
The Intricate Technique
This is very involved and involves you learning HTML and other website creation languages. If you already know them then magnificent, but for those who don't this is not an option. If you can handle the code, then you will need a database of coupon codes that is updated through affiliate scheme voucher code feeds and displayed in a directory.
The Straightforward Way
Assuming that most people are reading this piece because they do not have the required technical skills, the easy technique is the technique forward. But rather than getting involved in writing code or using a DIY web site builder tool, you should only install WordPress and use that!
There are 2 ways of doing this, depending on your skills. If you could handle the basics, then download the latest version of WordPress and FTP it to your web site. If this is past your skill level, then choose a host that advertisers the installation of WordPress in a few button clicks!
Next, hunt around the internet for a suitable free theme, download it and install it to you new website. Then you are up and running!
All that you now need to do is to sign up to one of the big affiliate system providers. There are plenty round the globe to pick from, depending on where you live. If you are struggling to find one, have a look on a couple of discount code web-sites for what merchants they are displaying codes for. Then search for that merchant and the word 'Affiliate'. Eventually you will find the systems these are listed on.
Once signed up, you will then be able to join the merchant's programs and then as new voucher codes become available you will receive emails. As these emails arrive, go to your website's admin area and start a new post. Make the title something that includes the merchant and coupon summary, for instance '10% off at this merchant'. Retype the content of the email, ideally writing a bit about the merchant to increase the word count so that the page is not too empty (if there are only a couple of dozen words on the page the search engines will ignore it) and use either the category or the tags as the merchant name - whichever is displayed in the sidebar of your blog. This then means that traffic to your site can with a single click view all codes for a merchant and is magnificent for optimisation!
You then just need to work on getting a few traffic to your website, however you have chosen to do that. There are ample of ways of doing this, just try out a few and see which of them work the best for you.