Teachers build connections with students by seeking and creating opportunities to mentor them: getting to know them as individuals by finding out about their lives and interests (while respecting their boundaries); offering support; and encouraging skill building and decision-making.
Supportive and respectful adult presence in the context of student-initiated and -led extracurricular activities provides an effective means for building connections with students. Taken together, the various facets of our role as adult facilitators of youth empowerment add up to mentoring, and all contribute to building connections with students.
The main things for teachers to remember are that they care about their students, meet them where they are at, and ask them what they need or want instead of assuming.