Start the FTB App and click on "Browse"
Now with the App open you will need to find the pack that you want to install. You can do this by browsing the top and featured packs or using the search bar to search for it. Once you have found the pack you would like to install, move your mouse over the pack icon and then click the download icon as shown:
If there is more than one version of the pack available you may be prompted to choose a version to install. The latest version is selected by default, you may need to select an older version if you intend to play on a server that has not yet updated.
The App will then go through the process of downloading and installing the pack, depending on your system and internet capabilities this could take up to a few minutes to complete.
Once installation is complete you should see a green "View Instance" button that will take you to the pack details page.
From this page you can manage your instance. The versions tab will show you the different versions of the pack that are available, along with the changelogs and server downloads for those versions. You can view a full mod list under the mod list tab. The settings tab will allow you to change the amount of RAM you would like to allocate to the pack, along with any custom Java arguments that you may want to use. You can also choose the default Java installation to use for this particular pack here.