There are many ways to copy the files from PC into your SD card. Simplest is the Android's native MTP mode, which you might be having trouble with detecting the device in Ubuntu/Mint.
You can use ADB as mentioned here by Izzy. Setup ADB and detect device on your PC (see Is there a minimal installation of ADB), open terminal and enter:
adb push <SOURCE> <DESTINATION>
<SOURCE> would be the file location in your PC like
DESTINATION would be file location in your Android device like
adb push ~/Downloads/OTA_Lollipop.zip /sdcard/
Some users report problems while setting up ADB in their PC. In that case, see this method by ykasidit.
You would need to install an Android app named MTP-Alternative USB drive. (See Method 4 for its detailed usage.)
Use Airdroid which I covered here.
If all the above method fails to work somehow, then try my guide here. See Method #1 there for MTP-Alternative's usage, or try my Method #3 there.
Note that all the aforesaid methods would work with Wi-Fi hotspot and USB-tethering.