All Bible quotations are from the King James Version.
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The Bible says what you must do to be saved (John 20:31; 1 John 2:22-23; 1 John 4:14-15). You must believe in Jesus as the Christ and the Son of God. To be “the Christ” means He is the Savior from sin (1 John 4:10). That means He takes away the punishment of sin. To be “the Son of God” means Jesus shares in the nature of God, and in that way is the same God as and is equal to God His Father (John 1:1-3; 5:18).
What does it mean to believe? The Greek for “you may believe” and “believing” in John 20:31 is pisteuó(1). It means “trust, put faith in, rely on[.]”(2)
Bible translators unanimously leave John 3:16, 3:36, and 20:31 with salvation just by believing(3). (Who can find one that doesn't?) The definition of “believe” in English hasn't changed in at least 46 years(4). It means to mentally consider something to be true. This is the only definition that works with both, because the Greek doesn't say anything about working.
Translators know that translating from one language to another isn’t perfect. They know that some things might be left out(5). Still, of course, a good translation can’t change the meaning.
Another way to say “believe” is “trust.” And it's not just trust. It's trust “in” Jesus. That means putting trust in Him.
The Bible says “whosoever believeth in” Jesus will be saved (John 3:16; cf. 1 John 4:14-15). The Greek literally means “everyone”(6). It’s “whosoever” and then only “believeth in” Him.
Why are you supposed to put trust in Jesus? To be saved. What saves you? Only trusting that He is the Son of God and the Savior from sin. All you have to do to be forgiven is trust in Him being the Savior from sin and the Son of God, and trust so that He will forgive you.
There might be a lot of ways. Two are explained here. The first is preferable for your relationship with Jesus Christ, because it comes from something you need to do with Him regularly.
You can know if you honestly pray to Him. Here’s why I think that: A person easily knows for certain if they believe they are talking to someone who is standing right in front of them. If someone believes in Jesus, they believe that they are doing just that (except Jesus is only spiritually present). If someone talks to Jesus and senses that He is real like anyone else they talk to, they think of Him like they think of people they definitely believe in.
You can know if the part of you that tells you when you’re thinking clearly or not clearly answers the question “Do I truly believe in Him, or am I fooling myself for some reason?” with “I really do believe in Him.” Here’s why I think that:
There is a part of someone that they think can tell when they are thinking clearly. That’s their perception of self. They rely on it to try to accurately know anything about themself. It is truly their perception of self, so they do really perceive what their self thinks.
If they ask this sense of self “Do I really believe in Jesus? I mean, is He really my Savior and the Son of God regardless if no one else I am around acknowledges that? Or, am I fooling myself for some reason?”(7) and it says “I really believe in Jesus,” they perceive what they really think.
This perception of self is what God uses for people to be confident that they are thinking clearly. So, it’s what God uses for people to understand the Bible. In fact, it’s what God uses for anyone to be confident of anything at all!
Therefore, to disregard it is to disregard what God uses for people to be confident of anything at all(8).