Soteriology is the study of salvation. It is "salvation theory" or the doctrine of salvation. It can be a sore spot of division, but there are some clear Biblical teachings which everyone should be able to agree on.
The first question is "Why is salvation needed?" or "What are we saved from?". This is an important question. It defines what our problem is, and influences what we need to do to solve it.
First off, we are not saved from illness and poverty. There's an excellent quote they play on the Way of the Master radio: "Anyone who says, 'Get saved and live a better life' - has never read the New Testament." (Unfortunately, I cannot identify the speaker). The Bible is clear, get saved and receive tribulation and persecution (John 16:33, the parable of the sower, Acts 14:22, Romans 5:3, Mark 10:30).
We are saved from Hell. But why are we in danger of Hell? For the average person, this seems unreasonable. Ask any 10 people on the street, and probably at least half of the them will say they are good people who deserve Heaven, not Hell.
But the Bible makes it clear: "For all have sinned, and come short of the glory of God" (Romans 3:23). God is perfect, and so must we be perfect. How many murders make you a murderer? How many lies a liar?
"murderers, ... and all liars, shall have their part in the lake which burneth with fire and brimstone" (Revelation 21:8)
Paul uses the analogy of a courtroom (how many laws do you have to break to end up in court? Is the judge impressed that you usually do not break laws? That you believe he is good? That you won't do it again?).
We are the defendants, and we are guilty.
There must be a price paid (more like our civil court than criminal). That price can only be paid by the blood of Jesus.
When we realize that we are sinners, in need of salvation, and that Jesus has paid our price in full, turn from our sins, and trust in God - we are saved. Our "criminal" record is applied to Jesus, and His perfect life is applied to us.
Another analogy used is that of a slave auction. As sinners, we are owned by sin. Jesus' blood "purchases" us. We receive the seal of the Holy Spirit as evidence of this "down payment" against an inheritance of eternal life with Him.