Just go to the website!
The easiest way would be to go to the hotel's website. The big hotels usually have their sites in English as well. If you see an "English" link on the website, press that. If not, try to look for 予約 on the website.
From there it is straightforward. You just have to input the days that you want to stay at the hotel and pick the plan/room that you want. It is fairly straightforward, so do not worry about making reservations!
For example, for the Intercontinental Hotel in Yokohama, the English website is: http://www.ihg.com/intercontinental/hotels/gb/en/yokohama/yokha/hoteldetail. All you have to do is go to "View Rooms/Rates" to make your reservation.