Hello there,
Visiting Japan is indeed exiting! Be it your first time or tenth time.
Let's have a look at the route's your be travelling. Here's a quick breakdown on how to travel them using the JR Pass.
Haneda - Osaka: First, make your way from Haneda to Tokyo station. You can use the Tokyo Monorail from Haneda to Hamamatsucho station (the last stop for the Monorail). There, transfer to the Yamanote line to Tokyo station. From Tokyo station you can use the Hikari Shinkansen to Shin-Osaka. Local trains run into Osaka city from Shin-Osaka. (about 4-5 hours).
From Osaka - Nara. Use a local train from Osaka to Nara station on the JR Yamatoji line (about 60 minutes).
From Nara - Kyoto, use a local line directly to Kyoto (about 60 minutes on a rapid service).
From Kyoto - Tokyo, use the Hikari Shinkansen directly from Kyoto to Tokyo station (about 3 hours).
Hope this helps,
Daniel