When they do that, you are building up your list because everyone who enters their name and e-mail address is your new prospect. OK, all that mailing list is not that hard and probably most of you already knew these steps. The bigger problem is how to drive traffic to your squeeze page and get those people who will be willing to give you their e-mail address and join your mailing list.
There are several ways you can achieve that. You can try article marketing - write and submit articles to directories to gain traffic to your website. You can try video marketing - making and submitting videos to video sharing mailing list websites and similar places with your links attached to gain more traffic. You could try forum marketing - joining a few of the most popular forums in your niche, contribute to the forum by making valuable and useful posts while promoting your website in your signature.
Or you could try with list builders. Also, there are other ways to build up your list but these are the most common ones. For mailing list me, all of those methods are extremely important and you should do them all. But, one of the easiest and more quicker methods are list builders which are, in general, membership sites where you can send your promotional e-mails to other members.