This reminds me of my first Linux installation. Glad to answer.
I'll divide my answer into parts so that should be an easier reference:
1. Ubuntu in 2 steps
Yes you can install a dual boot Windows+Ubuntu quite easily following the installation indications that you mentioned.
When you installed Ubuntu alongside Windows, you'll find 1 or more new partition on your hard drive, on which Ubuntu was installed.
Windows uses 2 partitions at least (one for the boot loader and one for C:), so that would mean you now have 3 or more.
2. Backup
The easiest way to backup files from Windows would be to simply copy them to the Ubuntu partition following these steps:
- Boot into Ubuntu
Open the file browser (Nautilus, the equivalent of Explorer) and search your Windows partition in the device list on the left. Click the device.
Find the files on the partition, and copy them.
3. Remove the Windows partition
This is easily done with GParted.
If you don't have GParted install it with
sudo apt-get install gparted
Open it:
gparted &
In GParted find the Windows partition, select it, delete it and click Apply.
Warning! After you do this, the data on your Windows partition is lost forever!
Mark the space empty, "Create new partition" somewhere and choose a name ("Data", for example).
You can format the drive as ext4 (if you plan to use Ubuntu only)
If you may want to move back to Windows choose NTFS.
Open "Storage Disk Manager" (for example by searching for it in the Unity search box). Click the partition you created and configure it to mount at boot.
Instead of creating a new partition and mounting it, you could also start from a Live CD/USB and expand the Ubuntu partition.
Feel free to ask more info if you need.