Learning how to create safe spaces for students to share their thoughts and feelings can be a challenge when you have so much else to accomplish in a class period. But there are some simple things you can do to make great strides in that direction.
Check-in Notes - Just before students leave class have them jot down on a piece of paper how they're feeling about the class, about their day, about the subject, about your teaching...whatever you choose to ask them. They can do this anonymously or with a name - and when you read through their comments you can get a sense of how they're doing.
Chills and Thrills - (one of my all time favorites!) At the start of class–especially when you can tell the students are coming in a little riled up–ask them to share a chill and a thrill. A thrill is something good going on in their world. A chill is something not-so-good. This simple exercise can do a lot to clear the air. I always made the sharing voluntary but usually got a good variety of students responding.
Assignments About Me - as often as possible try to relate assignments and projects to the lives of your students. This not only gives you a better idea of who they are and where their interests lie, it also makes any activity instantly more engaging for them. With a little thought you can make almost any project personal. If you want students to do a report on a famous person - make it a person they'd like become when they grow up. If you want students to demonstrate understanding of a particular math concept - have them write and solve a word problem about a situation in their own lives where they might need to use this kind of math.
Opportunities Outside Class - It's strange but true that the best time to get to know your students may very well be when they're not in your class. At a football game, after school, at lunch, during recess (if you have it), before school, between classes...these are some of the tiny opportunities you can seek to ask your students how they're doing, talk to them about their plans for the future, and get some insight into what they need to be successful in the present. Outside the context of your class students are often more likely to open up and the things they have to share can help both of you when class is in session!