How or what makes you think or believe that you know Jesus?
The same way I know other people and things. Through direct experience and meeting with him, and also through reading about his life and teachings. Some Christians also get to know him through a particular tradition, although this has not been my path.
If you can imagine a historical figure, say Einstein, who is no longer physically living, but you want to get to know him. There are three ways to go about this. First, you can read everything that was written by or about Einstein. Second, you can go the route of a medium and attempt to contact Einstein directly (I now, sounds fuzzy for Christianity, but bear with the analogy). Third, you can become a physicist and have a whole tradition of commentary and so forth that helps you understand the first way.
Well, in Christianity we have a sacred text that provides us with an account (the Bible, and non-canonized texts if you also are open to those) of Jesus' life and teachings. That provides us with a vehicle for the first route. For the second route, there is a long-standing tradition of direct experience of Christ. Some call this being born-again. Some call it being in the Spirit. Some call it recognizing the Light or Voice within. Some call it mysticism. Essentially, they are all describing coming to know Christ personally and directly in some way, such that Christ is poured into you and you are gradually changed- refined into a being that can become Christ's hands and feet here on earth. The third way is that we have a lot of different churches and traditions to help guide people through the first two ways, including ritual, commentary, and so forth.
I am primarily a Christian mystic, and it just happened that in my life, the second way came first. I first experienced Christ, and then I became old enough to study the texts, and finding a tradition that fit was always more of a challenge, though I try to read from a variety of traditions and also participate in ritual at church regularly.
I imagine most of the question is the definition of 'know'. Studying scripture, going to church, etc... might be one person's definition. I would place more stringent requirements.
As I don't know what these more stringent requirements are, I can't speak to them. I would guess perhaps you mean "know" as in you "know" your friends? I feel that I know Jesus and God pretty much the same way I know people in my life, except that my mind is much less adept at grasping what I experience of them. But if you think about it, even other people are more or less a mystery. We don't really know ourselves all that well either, if you really meditate on the self and who you are. What defines you? How do we know others? Well, then you get to Jesus and God... it becomes even fuzzier. I prefer to say I "experience" Jesus and God rather than I "know" them. But then, by extension, I would say I experience myself, my loved ones, my pets, etc. as well. I don't really know much of anything.
Personally, I think that's OK. I think God and Jesus Christ are mysteries to be experienced, not Being(s) to be picked apart and defined. The trinity, for example, is not a definition to me but a koan... it is a tool for meditating on the mystery of God, on spiritual relationship. I went through a phase in which I tried to nail everything down, stick with a tradition, define it all... but no matter how hard I tried, the instant I even tried to express in basic terms what my experience of God and Christ has been, it was inaccurate. Eventually I came to find that, at least for me, what is the heart of my faith is the personal experience of God in all manifestations (including Christ) and how this changes my life and spirit. It is in experiencing Love I learn to practice love, and therein lies the foundation of my faith.
A pattern that I see is that a person who claims to know Jesus, also claims that Jesus is God. Is there anyone who claims to know Jesus, and to separately also know God?
In a way, yes. I first experienced God in my life, and then Jesus Christ. I mean, I knew about Jesus Christ, but he was not my first encounter with God. As a child, I first experienced God as a transcendent, utterly non-human Being. Later, I experienced Christ as a guide, a more personal manifestation of this Being. Christ is my comforter, teacher, friend. He is my companion and brother. He is what I can cling to when I am in the throes of human pains and suffering; he is the manifestation of God that understands these things on a personal level. He is the part of God that can give me a hug, pick me up, hold me close. He is my Lord and my King.
But I have experienced more to God than that. This is where it all breaks down because I struggle to explain it. I am a trinitarian and I am not. I suppose the best explanation is that I am a panentheist. But I still think the trinity is very important and speaks to an essential Truth about God. It is, as usual, impossible for me to adequately express, and nearly brings me to tears trying to do so. It is an overwhelming sensation on my part that I am utterly at a loss to describe to others.
Suffice it to say that the trinity has very deep meaning for me and this has increased over time, in my experience as both a Christian and a Druid. But I do not treat it as a definition of God. So I would not say I know God as Jesus, or Jesus as God. I experience Christ, who was once the historical Jesus. I experience God, in various manifestations. I don't attempt to define how these are related or what the limitations are, and any time I do it isn't long before God comes to me in a way that stands my world on its head and causes me to be reconstructed...