"God helps those who help themselves" is probably the most often quoted phrase that is not found in the Bible. This saying is usually attributed to Ben Franklin, quoted in Poor Richard’s Almanac in 1757. In actuality, it originated from Algernon Sydney in 1698 in an article titled Discourses Concerning Government. Whatever the original source of this saying, the Bible teaches the opposite. God helps the helpless! Isaiah 25:4 declares, "For You have been a defense for the helpless, a defense for the needy in his distress, a refuge from the storm, a shade from the heat..." Romans 5:6 tells us, "For while we were still helpless, at the right time Christ died for the ungodly."
In terms of salvation, we are all utterly helpless. We are all infected by sin (Romans 3:23), and condemned as a result of that sin (Romans 6:23). Nothing we can do on our own can remedy this situation (Isaiah 64:6). Thankfully, God is the helper of the helpless. While we were still sinners, Jesus died for us (Romans 5:8). Jesus paid the penalty that we were incapable of paying (2 Corinthians 5:21). God provided the "help" that we need precisely because we could not help ourselves.
Apart from salvation, there is perhaps a way that the concept "God helps those who help themselves" is correct. As an example, if you asked me to help you move a piece of furniture, but then just watched me as I moved the furniture for you, I was not actually helping you. I would be doing the work for you. Many Christians fall into the trap of inactivity. Many Christians ask God for help, but then expect God to do everything Himself. They excuse this by pointing to the fact that God will provide according to His will and in His timing. However, this is not a reason for inactivity. As a specific example, if you are in need of a job, ask the Lord to help you find a job - but then be active in actually looking for a job. While it is in His power to do so, it is highly unlikely that God will cause employers to come looking for you!