There are two types of tutors:
1) Professional, licensed teachers who make structured lessons for you like in school and have a high price. I think this is good if you are a beginner and don't know what to study.
2) Tutors who are "regular people" tutoring as a side job, focus more on conversation, and cost half the price. This is good if you don't like structure and like to pick your own topics.
In the past, I got tutoring on a site called JOI (japonin.com) and it had structured lessons, but I hated it. It was stressful getting taught a grammar point and having to immediately make my own sentences on the fly, even if I was confused or never heard of this grammar point. And it was a group lesson, so I waited quietly for my turn, stressing about what I was gonna say and held everyone back if I was confused. I have a mostly great experience with Italki tutors, except once. The teacher was trying to force me to read Doraemon because she always did that with her other students, even though it was too easy and she decided on her own that I should only speak casually (not using ~masu verbs). I don't like being forced into a "one size fits all" approach.
Flash back to current me, I take 2 hours of tutoring on Italki almost every day. Italki has tutors living in the US and Japan so it's easy to find someone who has a schedule to fit yours. I recommend doing the 3 trial lessons available and picking teachers who have a preview video of them speaking English and Japanese.
Now for the meat of my post. I prefer regular cheaper, not professional tutors. I do not like structured classes, and I collect A LOT of questions about Japanese or Japan throughout the day on my own. I love picking what topic to talk about and how long to talk about it. I send the tutor links to public Google Documents that I made so we can both write on it. Things I like to do with the tutor are:
1. Before the lesson, translate a story in English I wrote to Japanese. At the lesson, have the teacher help correct the sentences. Ask "why" questions about grammar and for explanations in Japanese about new vocab. (This is essentially homework, because you are preparing for the lesson ahead of time.)
2. Find a story on a site like http://syosetu.com/
, paste the story on a Google Doc, and take turns reading paragraphs with the teacher. After every sentence, I immediately ask the teacher about new vocab and try to summarize what happened in the paragraph. (Make sure to write down what page you left off, though.)
3. Ask about culture! A native Japanese teacher is a perfect person to talk to. Ask about their high school classes, differences between America and Japan (I'm assuming you live in the US, sorry), and customs. You take turns asking about a topic, listen to the teacher, ask questions about interesting parts, and then tell about how America is different. (Other great topics are holidays, like Japan's Valentine's Day vs. America's; popular food/candy; tourist spots; stuff you saw in a drama/manga that you want to know if it's real or not; etc.) I like to tell my tutors about things that aren't popular in Japan like they are in America.
4. Talk about your day, a vacation you went on, a weird memory... Learning how to say this is important, because it's vocab that is relevant to you.
You can break it up. Imagine you have a 1 hour lesson. For the first 10 minutes, you take turns talking about your day or a trip you went on. Print out "help!" words like "Can you repeat that?" "Please write that down" and use it in Skype so you can keep a record on new vocab. Next, ask any questions about Japanese grammar/vocab you have (5 minutes). With the remaining time (45 min), you can split it in half. The first half can be translating a story you wrote, then the other half can be reading a novel you found online so you can both read it. You just tell the teacher that you want to switch topics or keep going on the same topic if it is fun.