I just did my 1st giveaway and I found my sponsor through Twitter. A lot of Esty merchants sponsor as well. If you see something you really like, offer to review something of theirs if they sponsor your giveaway. I ran mine for 7 days others do longer it's up to you.
I first started in January and I love it. It is so fun getting the heads up on products and telling others that they just won! Like Delaney, I started on Etsy. I went through several Etsy Stores and found some I really loved. I emailed around 10 of them and heard back from about 3. I hold all my giveaways 1 1/2 - 2 weeks. I recommend holding it that long if you are just starting, unless you already have tons of followers and know you will reach a good umber of entries. This is out of respect for the sponsor of the product and for yourself to have time to gain new readers etc. I didn't start out with hardly any readers though so I felt that was best for me.
Another way to get products for giveaways is just start contacting companies. It doesn't matter how little or big they are. It can;t hurt you! I remember someone telling me to do this and I wasn't so sure about this. I did it though and was surprised with the response I got. Check out some of your favorite blogs and see who sponsored giveaways there, that could give you an idea of who to contact as well. Don't provide your own products unless you REALLY love spending money and have plenty of it. Also be sure to always inform the company sponsoring the giveaway product that they will be shipping the prize to the winner. You should not have to put forth any cost for this, just your detection and time. What you are providing them advertising FREE they should know it would cost a lot more otherwise so your service is pretty generous. Obviously this is up to you, but there is no need to spend your own money.
Like I said, I am fairly new to this but have learned a lot form other bloggers and through the past months. I am more than happy to help you out with anything else you may wonder about. Hail2thesnowqueen (at) gmail (dot) com www.Hail2thesnowqueen.blogspot.com
To be know at this, you have a wealth of information! Thank you so much for your willingness to share ! I have already emailed someone and will do my first giveaway in April! I am still a little nervous so I will be contacting you!