When it comes to people sponsoring you, as in they pay you to advertise their blog on your blog, you should let them come to you. There is nothing wrong with making small announcements in your post that let them know you have sponsor slots open (as well as a tab with info/pricing), but make sure that your sponsor list is close to the top of your page. No one wants to pay for their ad to be at the bottom because chances are it won't get noticed.
If someone contacted you asking if you wanted to buy an ad slot on their blog, how would you respond? Personally, I wouldn't be impressed, I wouldn't view their blog and if I was already a follower, I'd stop following. It comes off as greedy and tasteless in my opinion to specifically ask someone to give you money to show their blog on yours.
If you want to sponsor someone, then you'd contact them. Sponsoring other bloggers is a good way to grow your readers, if you are willing to pay for advertising. Networking is free and if you make blogger friends they might add your button to their blog, but that shouldn't be your motive because...karma.
They come to me and I mostly turn them away, to be honest, because they're not what I want on the blog. Rather I see adverts for sponsored posts and offer my services to those which fit in with my blog layout and contents and see if they agree.