I use varying approaches to grading depending on the assignment. For example, homework is graded with a check, check plus, or check minus to represent completeness, occasional perfection, or incompleteness, respectively. Other materials like quizzes and exams are graded numerically.
I provide my students with the solutions to the homework after they are graded for review, but not for quizzes or exams. If students have any questions about grading, I encourage them to attend my office hours to review with me.
Working with an access assistant, we generate a detailed, typed set of solutions for all the assignments. This provides a rubric for the TA to grade the assignments, after which he/she enters the grades into the gradebook. I also have these solutions on hand during office hours in case students come with questions.
Since I'm unable to see the students' names on the graded materials, I had to find a different way to hand the materials back to my students. What worked for me was printing sticky labels with each of the students' names and using those to label each document with the help of my access assistants. The documents are folded in half to obscure the student's name and the grade and sealed with the matching label. The sealed materials are then made available with the lecture notes at the beginning of each class, so students can collect them on their own.