Homeschool unit studies are programs that incorporate all subjects into a single topic of study.
For example if you are doing a study of the arctic:
Math is one subject that is difficult to incorporate adequately in a homeschool unit study. I am not saying it can't be done. I'm sure there are some unit study purists who manage to incorporate math into daily studies. For supplemental homeschool activities, puzzle books or counting games can add some math for the younger set. IMHO more is needed.
If you are a creative and highly energetic sort this could be the perfect homeschooling method for you. Are you someone who loves to research? Are you someone who loves to plan and will be able to follow through on that plan?
Be realistic as to how much time you have to dedicate to this. If you are planning your own unit study, and you want it to be scheduled and organized. it can take quite some time to review and gather all the resources you want. Especially if you have children of differing ages you need to be sure they all have materials on their level.
There are many commercial unit studies available for all ages. You might want to try a few prepackaged programs to get a feel for how it works and the types of activities and supplements are available.
Remember though, that units can also be planned on the fly. Ask your kids what they would like to study and work with them to come up with a plan. Visit your library online, do a search on your topic of choice. You may just find a wealth of information that you didn't even know existed. Make friends with your librarian!
History is a natural for homeschool unit studies. Simply pick a time period of choice. Choose from biographies, historical fiction, visual dictionaries. Add in some documentaries and crafts. Often a cookbook for a time period can be found and you can add home economics to your list of subjects.
Make a list of these materials. Start working your way through them. Read, discuss, read discuss. Read fiction and nonfiction. Read to your children and have them read independently then report back what they learned. You might decide to read 3 biographies and 3 fictions, 1 reference book and 2 movies. Add in some writing.
If you are crafty, you are blessed! I'm not crafty. But if you are... do whatever projects strike your fancy.
As your children grow older you may find that they can take charge and plan their own unit studies.