What do you mean by "merge the two drives together"? Do you want to have one "virtual" partition on two physical discs? Then probably you should google LVM (I've never used it, so it's all I can say).
But why do you want to merge the two discs? If I were you, I would use the fast SSD for some selected data (for fast boot or whatever) and HDD for the rest. When they are merged together you can't control where your data is stored and you don't benefit from having fast SSD (unless you are very lucky).
If the reason for merging is that you don't like too many logical partitions in your computer then you don't have to worry: in linux you don't normally navigate with drives but with a virtual directory structure (see the next paragraph). So some smart mounting may be a solution: you can mount your SSD in some folder (e.g. inside another folder stored physically on HDD!) (or even divide it into partitions and mount in several folders).
Finally: if - as you said - you're installing ubuntu on SSD, then you can just use the standard schema: put your ubuntu ("/" directory called root) on SDD (24 GB should suffice since my old installation is 16 GB) and your home folder ("/home") on HDD. All your personal data will be stored in one place (home) and you will benefit from having system files on a fast SSD (dunno if it is the best way of utilising SSD, but for sure it is the simplest).