I have had several companies send me product to review. Each happened in a different way.
1. The company contacted me so that was easy.
2. I found a product in the store that I fell in love with and wanted to share on my channel. Before I did, I contacted the company and asked if they had any issue with me sharing it. They looked at my channel, liked what they saw and "approved" the idea. Now they send me samples of new products on a regular basis.
3. I purchased something from the Internet, I was really impressed with the product and hoped that I could do a tutorial for the website I purchased it from. I wanted to get it embedded for all of the shoppers. Anyway, I made the video, contacted the shop owner and sent her a link. Now she sends me product to use and show to my subscribers.
These aren't all small companies either. The Internet store is rather small. However the one I mention in the second example is a product line sold in Walmart and several other big craft stores.
I find that when I love a product, I am really inclined to contact the company and hope we can work together.
I have noticed that as my channel had grown more people contact me about reviewing products. I am not with a network btw.