When reciting the Office, the first thing to do is to be realistic. As a lay person, you have to be realistic about how much of the Office you can incorporate into your day. It may well be the case that you can work the full office into your day. The best advice I can give is not to try and do it all at once - if you are anything like me, you will be enthusiastic for a couple of weeks, then start to miss an hour here and there, and eventually let it all go, feel guilty at Lent and start over.
The best advice I can give is to start with one or two of the hours and commit yourself to saying them absolutely every day. I would suggest a morning hour and an evening hour. If you have anything like a normal 9-5 schedule, the day hours will be the hardest to incorporate into the schedule (unless you combine them with another hour), so start with morning and evening. Your mileage may vary, but if you are using a traditional breviary, I would suggest at the outset to pray Prime and Compline; though these two hours are the most peculiar in structure, they have the advantage of changing very little day to day. Let these hours become an invariable part of your routine before adding anything. Make sure you understand the outline of the hours before you add anything. Give this at least two weeks before adding anything.
If you are working toward reciting the whole Office, next I would add Lauds and Vespers, as these are very important hours. For the time being, I would ignore the Sanctoral cycle until you are comfortable with the structure of the hours. Just read Lauds and Vespers of the weekday for a week or two, until you are sure you can move on. Next, add Matins. Matins is the real heart of the Office, and can also be complicated, so again, ignore the Sanctoral cycle until you're comfortable. Lastly add the day hours. Terce, Sext, and None are identical in structure and easy to learn; however, given most people's schedules, they can be difficult to fit in.
Once you are comfortable with the overall structure of the hours, then you can begin saying the Office proper to each day. The important thing is to be realistic and to really internalize the hours into your day. You should get to a point where you really feel something is missing if you do not say the Office. If it becomes a part of your life, and if you internalize the structure of the individual hours, then moving to the propers is not terribly difficult. There will always be questions you will have - the interplay between feasts can get confusing, depending on the rubrics you are following. Fortunately there are several very knowledgeable people here who are always happy to help. Good luck, and God bless.