Hi agnis,
I have been searching for information related to this screen and I found this document: http://www.sainsmart.com/zen/documents/20-011-918/3.2LCD+UNO.pdf. I don't know if you already found that document, but it explains how to use the TFT screen with the Arduino UNO. There are some pins of the TFT display that are connected to the analog pins so you can check it. Since the Galileo has the same pinout of the Arduino UNO that could be useful to know how the display can be connected to it.
In the document there are some explanations related the code used, and the example used can be found here: The Desktop Contemplator - Nuts & Volts Magazine - For The Electronics Hobbyist. In that site you will find a download section to download the code example and some additional documents including a couple of datasheets that can be interesting to you.
They use a library named UTFT in the code. I searched for it and I found this site: UTFT - Electronics - Henning Karlsen. In there, you will find useful information, including the UTFT library. There are several examples for Arduino and PIC32. However here is also the bad news. I was thinking that the library could be used with the Galileo but it is written specifically for ARM, AVR and PIC32 architectures. Since the Galileo has a different architecture the library won't work.
If you still want to use this TFT display the option would be to write a new library to make it compatible with the Galileo, however that is not an easy task. I would suggest using another TFT screen. I'll recommend you to check this other thread where an user was able to use a TFT screen that you might find interesting: Re: 2.8" TFT V2 and Galileo Problem.
Regards,
Diego.