Upvote:5
The most unfamiliar thing for you will be in Tokyo/Haneda, and then in Osaka/Itami. Fortunately both are relatively small airports (compared to the other possible route, to Tokyo/NRT and Osaka/KIX).
Haneda Airport's International to Domestic Transfer page will be of interest to you. Basically the steps are:
May I suggest that while you're in Haneda International arrivals hall, you withdraw some money from an ATM, or change cash (exchange rate isn't too good though).
For ITM, check out this page and this map (PDF). Depending on where you're going in Osaka, if they're not picking you up, you can take the train, or the bus. Avoid taking a taxi, unless you're super wealthy, or on a gold-plated expense account.
Finally, I would recommend to order a prepaid SIM card before you leave the US, and pick it up at Haneda (if you have the time to drop by T1 first), or at your hotel. This will make your life much easier (if you have an unlocked phone, of course...).