I have had many people report to me over my career. In that time, I've had people share stuff they just shouldn't share with their boss. One shared about an abortion, one a bad breakup, one was stressed out over just having a few things in his role change. I had a guy completely lose it over college funding costs, and I had an employee share that he took a part time job because he isn't making enough money. When these conversations start I put down my pen, back away from the keyboard and just listen. I hurt for them, but it is not my role to provide advice about their personal lives. What I can do is provide support within the confines of the office benefits. I provide the outside counseling line that our company provided free to employees, and one I shared what was covered for FMLA leave. I've always kept these topics to myself and not used it against them...but I could have. I echo the advice above not to share too much.
"How was your weekend" usually means I want you to tell me what you did that was fun or interesting, but I don't really want to hear that your birth control failed when you stepped out on your husband so you had to get an abortion and she was in physical pain and overwhelmingly stressed.. Yes, that was shared with me, and our only connection was that I was her boss.
The best example of how to handle things was an employee that had some complications when her youngest was born (by then he was 15) who needed a hysterectomy. She came into my office and said she was facing a challenging personal situation related to her health. She wanted to know what I needed to know, as it would likely mean she was out of the office for a bit. I immediately told her I didn't need to know any details other than that it was medical in nature, and then we laid out the FMLA terms, including the part time return to work plan. I was happy. My wife found out about the nature of the issue later and shared with me, but I never knew and both of us (the employee and me) were happy to continue our work relationship without ever discussing the nature of her medical leave.
What does all this rambling mean? Your boss most likely doesn't want to hear all your issues. She may try to be sympathetic to your issue and help you out or she may just put you on her problem employee list. It isn't worth it to risk finding out which you have. It sounds like you may have a good one based on the comment of it going well. In the situation described above I'd call HR (or go to their SharePoint site) and see if there are any counseling benefits offered by the company. I'd call them first and talk through my issues. When discussing things with the new boss, I'd stay away from the reasons behind any of your work conditions, but let her know what you need, request any FMLA that may be appropriate, then I'd just speak about my availability and any reasonable accommodations I might need to do my job.
I'm glad it went well, but any others out there, be careful what you say to your boss. Even those who try not to let it influence them, it will. My opinion of the woman who stepped out on her husband will never be the same, and I have to fight myself to keep from letting it negatively influence my perspective of her work performance (which is above average). Don't put your boss in that position.