First, this question is about asking for a tutorial, and as far as i know googling "opengl tutorial" is enough to get you started.
Second, i don't recommend you to use such an old version of opengl, even if you want to support an extremely large range of computers, the 'modern opengl' (a.k.a. Opengl 3.0+) is widely supperted as well.
And imho learning opengl 1 is useless for any intermediate complexity project, because it lacks of many essential features (see framebuffer objects).
That said, if you give up with gl1, non power of two textures will be fully supperted on every machine.
Here I want to give you a fair starting point to solve your actual problem (this is not for lwjgl, though, and I assume gl3+ with shaders):
In opengl you don't render textures, you render geometry, so you have to draw a quad with the proportions of your textures.
To do this, feed a buffer with the data of this specific geometry and draw it.
Now it's time of shaders, you will need a vertex and a fragment shader, where you actually sample a texture object created before to output your quad filled with your texture.
Now, you are aware that with only what i wrote, you can't do anything, because all the details that you need to write a working program are missing, so