I am using a public guest wireless in a public building and it says:

Does this mean that logging into lastpass (I already did) or this website for example with my passwords would mean that a third party can see my passwords?

I can't even check my email on a public wifi because then a 3rd party can know the password to my gmail?

What steps to a 3rd party take to delve into privacy of users of public wifi?

 

If the site begins with http s:// , it is using SSL which is far harder to crack and generally not worth most people's time to do so, even on public wifi. So for example gmail is generally safe to check in public because it is always using the https connection. This website does not use https by default so sniffers could see your login info if they were looking for the right things.

 

If you're very paranoid about security in public access points, you can check out a VPN solution. Basically, it's a tunnel whose two points are your laptop and wherever the VPN server is located; everything else is blocked from seeing/interfering with your internet traffic. Harder to break into than HTTPS, but HTTPS itself is pretty secure as is.

Another option would be to use your phone's 3G/LTE connection, if you have one. Even if you haven't paid for tethering service from your cell phone company, you're still legally allowed to do so. See ( The Right to Tether: What the Verizon/FCC Settlement Means to You)