It seems common in Christian communities (and in questions on this site) for people to say they have been saved. What does someone mean by this when they say it? How would I know that I have been saved and is there a particular moment of saving I should be able to identify?
In order for the language of being "saved" to make sense one has to understand what we are being saved FROM. There has to be a before and after scenario. We are saved from the wrath of God. Those without faith in Christ are described as children of wrath.
Consider this passage that uses the language of being "saved" including some details on our original position before God, the change that happens, and our final standing after salvation as well as the key operative bits on how that actually happens:
That wrath was metered out on Christ (Isaiah 53:5) and by bearing this punishment and separation from the Father he claimed the right to make us Sons. He transferred us from the domain of darkness into the light.
Returning the the language of Ephesians above, "being saved" means being made alive, to be raised up with Christ. A few verses after the Colossians passage above it talks about how God reconciled us to himself through Christ.
To "be saved" thus means to be rescued from the wrath of God, made alive in Christ and reconciled to the Father. The pre-salvation scenario thus has us as an object of God's wrath, the post-salvation scenario has us as objects of His affections and co-heirs with Christ.
The Roman Road is a good "path" of sorts for receiving salvation, but it is Romans 10 that is especially appropriate for this question.
I can't say it any better than these verses.
After we all die and we all stand before Christ to be judged for what we have done, some people will fail the test and be sent to Hell. While others will have succeeded in this life, be declared righteous and right with God and go on to live with Christ for the rest of eternity.
To be Saved by the blood of Christ means that you are free from the Wrath of God's Justice
In order to be saved you must: Does believing in Jesus Christ make me a Christian? Or do I have to do something more?
To know that you are saved, look here: How can I be sure someone I know is going to Heaven?