Google drive is indeed an excellent way to share files but you don't need to give anybody your password.
They can simply do it via their google account like this:
https://support.google.com/drive/answer/2494822?hl=en
If they don't have or wish to have a google account then dropbox is another popular storage/fileshare system that give free storage.
Microsofts Onedrive is another good one. There are of course many others and very handy to have.
These storage/fileshare systems are good as you can easily give out a link in future without uploading the file each time. You can also control the access by password.
If you want a statightforward file share only (i.e. No long term storage) then 'wetransfer' is a good free service
https://www.wetransfer.com
Don't bother with the mobile app. Just use the website- it's imply uploads your file and then send an email with a link to the other person- the link expires in 7 days (or so can't remember for sure). The other person then just downloads it to their machine.