First, you will want to click on the link you want.
That will open a page that looks somewhat like this...
You will want to click on that box with an arrow coming out of it on the bottom right.
Once you click on that, you will have three options. The middle one is to share the link which you want need right now, the top and bottom options are the ones you will want to look at. The first option on iPhone is to open it in Safari. I know for a fact that the giveaway widgets will work on Safari, so that is normally what I use for quick things like this. The last option is to copy the link. If you copy the link, then you can then go to the browser of your choice, and past the link into the address bar. I normally use Chrome for that.
If you have any other problems, please let me know.