The output from
fdisk shows you have 4 partitions on one drive, the first one is bootable (likely where your system has been installed to) and the third one is useable as swap.
fdisk only shows the partitions, not the filesystems on those partitions. To see the filesystems use
sudo parted -l /dev/sda or
sudo blkid -c /dev/null /dev/sda*. If they do not have a filesystem you first need to format them with one. This can be done with the
mkfs.* tools (warning these tools will destroy any data on the partitions they format). For example, to format your second drive as ext4 run the following; only if you are sure there is nothing on that partition already.
sudo mkfs.ext4 /dev/sda2
Linux, unlike windows, has a global directory tree where filesystems can be mounted. By default linux distros mount your system partition to the root of this directory tree (aka
/, or the root filesystem). Other partitions can be mounted anywhere you want. You can see a list of mounted filesystems and where they are mounted by running
mount. On modern distros this will show a lot of virtual filesystems, you can filter these out by running
mount | grep '^/dev'.
To mount a filesystem to the directory tree you can run the following:
sudo mount /dev/sdXY /path/to/mount/point
For example, to mount your second partition (assuming it has a file system on it) to /mnt/p2 (this is a typical location you that internal/manually mounted filesystems are placed; but it can be any path of your choosing) run
sudo mkdir /mnt/p2
sudo mount /dev/sda2 /mnt/p2
Now any file you write to /mnt/p2 will be written to your second partition. This will only last until you reboot, to make your system remount it at boot add the following line to
/etc/fstab (assuming it is formated with ext4).
/dev/sda2 /mnt/p2 ext4 defaults 0 0
To test this entry you can unmount it with
unmount /mnt/p2; if it is mounted. Then run
mount -a to mount everything listed in
Traditionally internal drives are setup with way on linux as such only root is allowed to do this by default so your gui file browser cannot, but the feature that lists partitions is included for removable media, which users are allowed to mount on modern linux distros. It also gives you quick access to the root of your filesystems once mounted. It is far easier to just configure the drives to mount at boot then to allow users to mount them at will.