Multiuser winform application and one single database, best approach?

I have a winforms application that it's used by multiple users and this application manages a single database. Right now the application has a DB connection opened in his entire life cycle and the users can make a huge amount of things that involve the modification on this single database. The database doesn't have FKeys and many times the application throws exceptions involving transactions locked.

So i want to change my database-connection-management logic to a better one. I though in EntityFramework but i don't know if this will work with a multiuser application.

What's my best solution for this?

INFO: In my solution i have a DataConnection project that works with the connections and the calls to the DB. I'm using DbConnection, DbCommand, DbTransaction for the DB calls. The DB is under SQLServer 2012