1. Once you've landed a TT job, you cannot rest on your laurels. The quest for tenure begins before you've got your books unpacked. Seriously. Hit the ground running, kid. (If you're in a department that lets you go up for tenure early, this is doubly true.)
2. Find out what the specific tenure requirements are for your school and department. Start doing those things right away. Departmental committee work. Some number of p-r publications. A book. Grants. Teaching. If your dept doesn't have some kind of orientation for new faculty, talk to someone on the P&T committee about what you have to do.
3. Keep track of what you do. I find it useful to keep a yearly log of my work activity, with dates, brief description of activity, and time spent. It includes things like meetings, guest lectures, conferences, papers submitted and accepted, papers I reviewed for journals, interviews and promo stuff, training, etc. It just takes a minute to enter the info, and when it comes time for the annual P&T review, it's handy to have it all there in front of you.
4. Keep a "self-promotion" file of stuff that supports you and your work. Print out nice emails from students or colleagues, copies of favorable comments from student evals, reviews of your work, awards and recognition, those stupid certificates you get for completing training, etc. Put notes in there about stuff you've done for others (e.g. helped a student get an internship). If you have anything that shows how awesome you are, put it in the file.
5. Keep your CV up to date all the time. Add all the stuff you never had on it before, like departmental service.
6. Keep track of when/where your papers are cited (I use Google Scholar for this) if you're at a research (or other) school that cares about that. If your papers are not listed on philpapers.org, submit them yourself.
7. Volunteer for the minimum number of committees you can get away with, and volunteer for the ones that are likely to meet the least often. You will not get tenure just for being that person who volunteers for everything and publishes nothing. Here it pays to know what you're expected to do by your department (e.g. smaller departments may expect/need more committee work from each individual, etc.)
8. Find a trusted mentor in the department, a senior person who can advise you on tenure-related matters, fill you in on departmental politics/squabbles/history/culture. Someone you're comfortable talking to. The first several faculty meetings are bewildering. I didn't know what the hell people were talking about half the time.
9. Find a focus in your research.
10. Make time to write/do research in proportion, more or less, to how important it is to tenure. This can be especially tough in the first year, if you're teaching new classes and doing preps, but it has to be done. You hopefully have some pubs in the pipeline already, so that one or two of them will be published in your first year. But if you don't do any new work in the first year, your pubs will be scanty to nonexistent in your second year, which is probably when your first probationary period will expire and your first review happens.
11. Build a network/alliance of people in your department or school (for social and professional support) and also start building a network of people nationally/internationally who can support your tenure review by serving as external references. Join the relevant professional societies/groups and go to conferences. Join faculty groups on campus that are relevant to your interests.
12. Juggling work and family is tough, especially when you're moving to a new community and don't know anyone. I wish I had excellent advice on how to do that, but I don't (although it is super helpful if your kid(s) are in school or daycare). Try to make friends with other people in the department who can tell you about useful resources, places to go, reliable daycare, good doctors, dentists, veterinarians, hair salons, etc. Taking care of that day to day stuff can suck up a lot of time when you first land in your new town.
I reckon others will have useful advice. Or questions. Chime in.