I need to redirect my users from my website to the Salesforce community.How can I use their username and password from my website and pass it to Salesforce community so that users are not asked to login to community?
Any help is appreciated.
When doing this sort of thing you do NOT retain the username and password detail for forwarding - this would be a massive security no-no. Instead you use some form of "Single Sign-on". See the Salesforce documentation on what they can support. There is also this article about configuring SAML for communities.