From a students perspective:
- Try to establish the students goals AND re-evaluate these after some number of lessons (just to make sure that goals haven't changed).
- Have something prepared ahead of time that you can fall back on if you finish going through what you originally planned for the lesson or if the student is not clear what they should do next. This could be as simple as a listening exercise where you can tell them a short story (at the students level of course) and have them respond with what they heard (using the target language if level is appropriate).
- During conversation practice, try to keep your student at the edge of their 'comfort zone'. i.e. if you are speaking slowly and everything is understood, ramp up the speed slowly towards native speed until comprehension is lost again (or if speed is not a problem, ramp up the vocabulary). As a student I know it feels a little frustrating to always be in a mode of not understanding absolutely everything, but it also means I have the opportunity to learn something. If I'm too comfortable, I'm probably not learning anything.
- Assign a little homework so the student has some motivation to learn between classes. This can be as simple as listening to a short video in the target language or learning one or two new verbs in a particular tense so that it can be used during the next lesson.
- Correct mistakes, but don't dwell on them unnecessarily or berate the student for making the same mistake multiple times. Make it clear that mistakes are part of learning and the more we make, the more we learn. As a student, I want to be able to speak 'with abandon' and not be overly concerned if I make mistakes. Yes, I want to correct them eventually, but I also just want to enjoy the experience of speaking in a foreign language and be understood as best as possible. Stopping every second word and going over the mistake in detail could be very demoralizing.
From a students perspective:
I actually have a couple of teachers I use on a regular basis and I use them for different things and in different ways. However, what they all have in common is that they are incredibly pleasant to talk to. That's what I look for first and foremost. The conversation has to flow naturally and not feel too forced.
What I also find very important in a teacher, is flexibility. I do a lot of studying on my own and have a pretty clear understanding of my weaknesses and areas I need to improve in. For that reason, I generally prefer to let the teacher know what I want to work on, instead of the teacher deciding what activities we're going to do. Some teachers lack the flexibility to be able to do this and seem to be stuck in their own workflow. That might work for some students, but definitely not for all.
One exercise I particularly enjoy doing and which I think has helped my Spanish a lot is reading together with my teacher. It especially helped me when I was a beginner, but I still find it incredibly helpful now. The way we work is that I put a ebook on the screen, we share the screen and I read out loud. If I don't understand something, the teacher explains it to me in SPANISH ONLY. This has been incredibly helpful for my vocabulary, pronunciation and even for learning grammar.
Unlike Vince, I really don't want/need homework assigned. I do more than enough studying on my own. So that again, depends on the student.
One thing I absolutely LOVE is being corrected. Even though I do of course get frustrated when I mess up too much, I badly want to improve, so love my teachers correcting me. I feel that most teachers don't correct their students enough. This again will depend on the student of course. Vince mentioned that stopping every second word would be demoralizing, whereas for me, I would want exactly that.
In short, there's nothing more important than getting to know your student!
What to do to make your students feel relaxed depends on "chemistry" between you as a teacher and students, because everybody is different with different personality, character and so on. A lot of patience, pleasant and calm attitude, but with mutual respect and mutual aim of working towards student's goals and needs.
To attract student's attention is more complex question. For me it's a matter of beeing focused on one thing no so long, that's why I prefer structured lessons with various activities during classes. Also, it is good for me if the teacher takes me outside my comfort zone and makes me think on my feet. But, It migh be something totally different for the others.