I need to know what can I do to connect the internet If I have the following message: WEAK SECURITY (WPA)

you can connect anyway, that's a warning.

Change settings in your ROUTER to a better encryption method, or get rid of that antique and get a more recent Router.

if you were unable to load any web pages because of DNS issues, that is a completely different issue than the one you raised.

WEP WPA and similar encryptions are applied to the messages from your computer to/from your Router, so that nosy neighbors to not read or intercept your data including banking and credit card and email data. This Encryption is NOT actually required to make a connection, but it is certainly Prudent to encrypt that part of the connection.