How do I get the new prisoners into my prison?

Solution 1:

You have to hire guards. The guards will automatically pick up the prisoners and escort them to the holding cell. Before that, the prisoners will not take any commands from you regarding cell assignments. Once the guard has escorted the prisoner into the prison, then you can assign cells by selecting the prisoner and right clicking (although they will automatically use the cells without you having to micromanage this step).

Solution 2:

Click on each prisoner and then click on the cell you want them to stay in.