I have read MongoDB's replication docs and MySQL's Cluster page however I cannot figure out how to configure my web apps to connect to database.
My apps will have connection information, database host, username, password etc, however, even if there is multi server function, should I need a big master that has a fixed ip that distirbutes the load to servers? Then, how can I prevent single-point of failure? Is there any common approaches to that problem?
Features such as MongoDB's replica sets are designed to enable automatic failover and recovery. These will help avoid single points of failure at the database level if properly configured. You don't need a separate "big master" to distribute the load; that is the gist of what replica sets provide. Your application connects using a database driver and generally does not need to be aware of the status of individual replicas. For critical writes in MongoDB you can request that the driver does a "safe" commit which requires data to be confirmed written to a minimum number of replicas.
To be comprehensively insulated from server failures, you still have to consider other factors such as physical failure of disks, machines, or networking equipment and provision with appropriate redundancy. For example, your replica sets should be distributed across more than one server or instance. If all of those instances are in the same physical colocation facility, your single point of failure could still be the hopefully unlikely (but possible) case where the colocation facility loses power or network.
