How do you get to your deep work session if you have meetings and other chores together with colleagues all day?

The best way is to schedule time for your deep work. Make it just as important as those meetings and gathering time with colleagues. Your work is important, and you have to be firm with it to get things done.
Also, if you write out what you need to accomplish during that 'deep work' session. You'll be more likely to get that work done in the allotted time set aside for those that deep work session.

I make my meetings and chores and social time my deep work. I completely focus on it and use my tactics to not get distracted.

I have not have such situation but I guess meetings can also be a deep work session too. Do not check your phone, make notes and prepare agenda. Keep your focus on it.

I get ready a little bit at a time throughout the day. I get my deep work project together piece by piece in intervals so that by the time I’m ready to sit down and begin, everything is ready and waiting to go.

It’s always changing by the day. Some days deep work is an option and sometimes just knowing that i’m doing my job even if it’s running around helps me consider it “deep work” that is part of my work day. Sometimes I will also have Deep work before I get to my job just to work on either something I’m passionate about or other to do’s. At work your always being pulled left and right, if it’s not letting you get to what you need to do, try letting your co-workers know that you need some time to work on what you are prioritizing.

Block time on your calendar. Come in early or stay late. Work more efficiently and/or longer. Say no to time wasting requests or meetings.