Public giveaways have many entries, as you can see this one, for example, was set only for one day and over 3000 people entered it already. I don't choose the winner, the site automatically does that randomly from the pool of people who entered the giveaway.

You cannot guarantee that you will win the giveaway you've entered. However, there are ways to improve your chances of winning.

1. You should find and join Steam groups which are interested in giving away games. Go into Discussions on Steamgifts and see which groups fit you. If you join a group and refresh your Steam sync (which you can do by clicking an arrow in the right corner and selecting "Sync with Steam"), you should see new giveaways, reserved for your group with less people in them.

2. Level up your account. There are giveaways that require a certain level to enter them, perhaps you can see on the main page Giveaways with things like "Level 1+". You have to make giveaways to level up, but to achieve level 1 you just need to give away one game which gives any contributor points (when you start a giveaway and choose a game it has 2 stars, 1 star or no stars, if a game has 2 stars it means, that it doesn't give any contributor points, no matter the price). Just having Level 1 gives you more giveaways to enter.

3. Explore the Discussions of Steamgifts, some people organise puzzles, giving links to their giveaways.

Hope you win sooner or later, just don't give up.