But let me try to talk you through it.
Step 1 - Analysis/Requirements:
Get your requirements right, what should your system do, what functionality.
So, GSM functionalities and SD card savings (in short).
One of the requirements would be that's it on an Arduino (atmega 328P).
Any other hardware requirements?
Step 2 - Design:
Check the possibilities with the Arduino, 1 hardware serial and multiple software serial connections. One hardware SPI/I2C I believe.
SD cards often use SPI connection and GSM units most likely use serial.
So this works great. Check some tutorials on SPI and (arduino) serial.
Step 3 - Wiring up
Wire everything up, as defined in the datasheet of the devices. Cross the Rx and Tx lines. Put MISO to MISO and MOSI to MOSI accordingly.
Be sure everything has enough power (GSM modules typically draw a lot of current when sending/connecting). Usually, if you find out that two devices are attached to the same pin, there might be something wrong (unless you can declare how they're seperated or why this is the case).
Step 4 - Implement
Well, you stated you're good at programming, so I'll leave this open for you.
But mind that it's only one of the three steps, so you should look at some tutorials, it'll learn a lot faster than asking everything. Try to get a bit comfortable with your thoughts, base them on things you have learned.
So this shouldn't be an issue? Those pins aren't shared? - user1833028
Things like this can be found in the device's datasheet and if you follow some tutorials you'll see that they're different and why.
Also, what helps for me often, is to try to seperate this 'big' project into two smaller projects.
Try to get the GSM working and after that you go for the SD card reader.