To start off with, the server needs to be able to share its files. If this isn't enabled, your other computer can connect to it, but it won't be able to access this. This is best done by establishing a specific user account that has full privileges, but that's password protected. To create a new user account, select the 'User Account' panel in the Control Panel. Then, create it and assign a password.
Then, you'll need to share the folders that you want to transfer. It's best to just allow overall access to everything, but Windows will still protect some important files, like your user folder. You'll have to share it manually. To share any folder or drive, select the 'Sharing' option in the 'Properties' menu that's accessed by right-clicking. Then, click Advanced Sharing and select users from the data to be searched. Once you've selected users, another window will open. You'll need to click 'Find now'. It will display all of the users registered on your computer. Once you've selected the right account and given it the right privileges, click 'Apply' and close the windows.
Then, you can connect to your server computer quite easily using the path that you've established. These paths will be in the following format in Windows Explorer on a PC: //computername/C if you've shared the entire C:\ drive. You can find your computer name in the 'System' information if you don't know it.
For Mac computers, you'll have to select 'Connect to Server' in the 'Go' menu of Finder. Then, enter the computer name. Once this is done, it will ask you to enter a username and password. Use the ones of the account that you've created for this task.