There are a few possible solutions for using an SSD as a cache device in Linux (in the same way that Intel Rapid Storage Technology works).
The two leading methods are to use the logical volume management subsystem (LVM), or bcache.
I've had performance problems with LVM (but only on large volumes > 10TB), and a few stability problems with bcache (although all fixed with newer kernels).
That having been said I currently use bcache on a handful of machines (including 3 servers) and the performance increase is dramatic with some workloads.
Neither solution is very simple to setup unfortunately, and I'd advise using newer kernels - such as those supplied with Ubuntu 16.04 or even 16.10 - with either option.
This guide by Redhat-employee Richard Jones outlines the use of LVM and retrofitting it to some existing LVM installations.
A simpler solution (probably lower performance overall and possibly better reliability) would be to to put both your root filesystem (/) and swap on the SSD, with other data on the hard disk drive.
Unfortunately, whilst this is easy to do with a new install of Ubuntu via the installer, re-partitioning an existing system like this is also not a straightforward operation, but there are guides online to this (or you could always ask a new question here).
Whatever you do (use the SSD as a cache or "straight" storage) you should use fdisk or gdisk (or other partitioning tools like gparted) to remove any existing Intel RST partitions, and partition the drive.