How to pass values between asp.net web pages? and what is the most secure way?

Many ways:

1- Query strings pramaters and this way not safe as hackers can use it for gtting you data using hacking cripts.

2- Session variables: this way is more safe as it is most of the time used in server side code.

3- Cookies.

4- Application global variables.

you can use the cookies URL query stringSessions the most secure is the session cause the user can't erase or delete it  or modify in it you gove your application the session timeout 

Same Domain -ReadOnly Cookies with encrypted values along with AntiXsrf Token to prevent session hijacking.

Cross Domain - DataBase with minimal priveleges required. The web pages that need to read the data should only have READ rights. Encyrption depends on the sensitivity of data.

I recommend using Session variables along with Global variables (declared in Global.asax). They are server side methods so your data is safer than in query strings or cookies which are client side.

you can pass it by query string  with using encryption methods

there is many way to pass values : 

1- QS 

2- session 

3- cookies 

4- profile 

for me the most secure way is profile