So you've decided you need to provide someone in your raid team with some constructive criticism. My first word of advice: put that thought on simmer on the back-burner for a while before doing so. Seriously. No matter how well-intentioned, "constructive feedback" given in the heat of the moment is rarely effective. Instead, take some time to think through what you have to say to the person, and how you're going to say it. Here are some thoughts to guide you through that process.
First, Evaluate if You are the Right Person to Give the Feedback, and If It is Warranted
Once upon a time, I was filling in on a ToC25, healing on my shaman. An elemental shaman in our guild, mid-Jaraxus fight, started telling me everything I should be doing differently. On my alt. In the middle of a boss fight I was healing. This person was just another teammate. Not the raid leader. And I wasn't failing either mind you-- my shaman was 3 out of 5 healers, which I was pretty proud of given her limited play time that expansion and her crappy gear. This unsolicited criticism was ill timed, came from someone who had no business telling me what to do, and was directed at an alt that was actually doing just fine. This was a great example of how NOT to give constructive criticism.
In general, if someone is playing an alt to fill in for a role your raid needs, you should consider carefully how you give feedback. The player is less comfortable with that role generally, and is doing it as a favor to the raid. If you did want to help them boost their future performance, it would be appropriate, after the raid, to say "hey if you think you are going to be healing on your shaman a lot moving forward, I read a great blog post on healing you might be interested in."
Make Sure You're Providing an Expert Opinion, Not Just Your Opinion
Yup, that's right. Holding the title of raid leader or guild leader does not, in fact, make you an expert in every class and spec. If you have a hunter who is struggling, have your guild's best hunter talk to them. No one wants to hear someone who doesn't play their class regurgitate a well-meaning blog post they read somewhere, and being told to "just do that." Likewise, no one wants to be told how to improve by someone who uses another class/spec as their example for what to do. Each class and spec is different, and takes different finessing. If you don't have an expert in your guild on that class, do some online homework: start with Elitist Jerks and from there fan out to class and spec-specific resources. If you're not sure where to start, WoW Insider has a nice big list of WoW resources, including bloggers by class.
Praise Publicly, Coach Privately
This one should be obvious, but I have many times heard a raid leader berate a player and give them detailed instructions on how to improve in the middle of a raid, over vent. this is fail. How would you like it if your boss came up to you, in front of all your coworkers, to tell you you were doing a sucky job and should change X, Y and Z immediately? Yes, WoW is not a job, but the scenario still applies. No one wants to be taken to task in front of their peers. By doing that, it is unlikely that even good, well-intentioned advice will be heard by that player. Instead, they'll remember how they got chewed out by that jerk (YOU) in front of their raid team.
Make Your Feedback Specific and Actionable
Bad Feedback: Your DPS sucks, improve or we kick you from the raid team.
Good Feedback: Elitist Jerks is modeling a player with your spec and gear level at about 2k DPS higher than we're seeing you perform. I think we can do some fine tuning to your spec/gems/enchants/rotation to get you to where you need to be.
See what I did there? I gave specific feedback on what needs to be improved, and by how much, and laid out a possible check list to start with, and offered up a partnership with the person to help them improve.
Be Sure to Praise the Improvement
Once you give the feedback and support, and the person improves, you have one last constructive feedback task ahead of you: Praising the person for their improvement. This reinforces the change and shows the player that you are paying attention, and are aware of the efforts they made, and their progress. If you don't say anything, the player can feel as though they wasted their time and efforts trying to meet your standards. It's a small thing to do and doesn't take much time, so make sure to acknoledge your teammate's progress.