So you found a critique partner. Either through the match up i host here on my website or through some other means. Congrats! Putting yourself out there is a big step, and finding someone to work with is the hard bit and you've already done it!
Now for the fun bit. How you proceed with your new CP is really up to you, and each partnership will be different. But here's what I'd do, if i were in your situation again.
1. Chat a little over email. If i matched you up, I've already given you a few things you might have in common. Tell each other a little about where you're at in your writing journey, talk about your WIP or the books you've already published. Ask each other what you're looking for in a partner, and what you can offer.
2. Swap a sample chapter or two. Once you've gotten to know each other a little, put your big girl panties on and send off your work. I know! It's terrifying, especially if you're new to writing, but this is honestly a vital step. Take a few days and critique each others work. Remember! A good critique not only points out the bad things in a piece of writing, but also praises the good! If you can, give examples of how your CP might be able to change something to make it better There's no point saying, "I hate this paragraph." Tell them why.
3. Read over your critique. Yep. Take a deep breath, because this might sting a little. I've been working with my CP's for about 18months, and I STILL am terrified to open their critiques, even though i know their comments ALWAYS make my work stronger. Read over it. Then step away for twenty four hours to let your emotions settle. It always stings most as you read, but over the next few hours, let their advice sink in. It's probably not THAT bad. Don't let pride get in the way of becoming a better writer.
4. Talk about your critiques if there's anything you don't understand. Ask questions. Don't get defensive and keep an open mind. This is just one opinion. You don't have to take every point on board, but you should see value in at least some comments your CP is made.
5. Keep going! Or not. If you're both happy, fantastic! Keep going! Add each other on facebook, or twitter or some other place and make a commitment to check in with each other at set times. Once a day. Once a week. Whatever suits you. But if you honestly got your critique back and saw no value in it, or you found you honestly couldn't critique your partners work fairly, don't be afraid to thank them for their time and move on. These things only work if both people are on board.
I really hope your new partnerships work out. If they do, be sure to let me know! In a few months time, I'd love to feature you here on my site. And if not, don't despair. There will be more CP match ups in future. Follow any of my social media or hit me up with a friend request on Facebook so you don't miss the announcement.