To copy files between your computer and your RPi, you can use a USB flash drive. However, it is also possible to do it remotely.
Windows: Open MobaXterm (see Software) and log into the RPi using SSH (see Connecting with SSH). When you are logged in, on the left hand side, you will see the folder structure of the RPi. You can copy files between the RPi and your computer by dragging them.
iOS: First you need to do some setup. On your laptop, open "Finder" and then click "Go" and "Conect to Server ...". A new window will appear and in the "Server Address" type in the RPi IP address and click "Connect". In the window that appears next asking you to select the volume you want to mount, select "pi" and press "OK". After connecting, on the left hand side of the Finder window, you will see a new category called "Shared", and under it your new connection. This completes the setup.
Click this connection and you should see the folder "pi". If you double click it, you see the files on the RPi. You can transfer files by dragging and dropping.