Start with your local paper because the odds of winning will be better. It is very likely they have a website, go to their website and look. Some websites are easier to navigate than others. The companies want to keep you on their site as long as possible. You may find a tab that says, 'giveaways,' but sometimes it may be under titles such as fun, or even entertainment.
You can also type in your favorite magazine titles, and they will usually have ongoing weekly or monthly giveaways.
This also holds true for television programs; they often have links on their pages for giveaways.
To find several in one place, there are websites that have links to various giveaways. Remember though, the people who visit those links are 'hardcore' sweepers and will often be entering the maximum number of times, so the odds of your winning will be less.
Another place I found is Wikipedia. If you type in 'Magazines', you will get a list of many magazines, and some of these will be running giveaways. You can also do the same for newspapers. Just make sure you are eligible to win before you enter. Some regional publications may say you have to be within a certain area or pick up the prize in person.
Also, if you are running an ad blocker, you should switch it off as many companies are promoting their giveaways on other sites, and you won't see it if you have an ad blocker.