
So let's start with the first render:

As you can see, a box, nothing else, and a default material and light. Not interesting.
Let's apply some "wood" texture from the presets:

I can't say I'm happy with the look, first of all the scale of the texture is wrong. Let's try to resize it:

Well... it does look somehow a wood... but a really poor one. This kind of texture is called procedural, which basically is done via a mathematical formula to archive some look. You can get good results, but it will take you a lot of tweaking. Usually taking a picture is a better option. Let's see of it looks with a wood plank texture based on a picture:

Looks much better, but it can be improved with something called "bump map", it's basically another image applied on the box which defines small height differences:

If you watch carefully you will see that the bump map added some... features on the surface.
Another kind of texture map to play with is the specular map, which defines how shiny an area is:

Again the difference need to be carefully checked, but it does some difference.
Now, the cube does look better, but still, not really all that interesting. Why not try to add some more.... For that I work on the texture map, with the help of photoshop, but any image editor will do the trick too:

You see the edge of the box uses like a different texture, the texture map (the image) is the following:

and the bumpmap:

You can use them for your own trials if you want.
The result is not bad, and could already be used as is in a game. However I would personally add a little bevel on the edge which follow my texture:

the model is now like that

To finish my texture work, I would consider making the faces different, for it, a good stencil (some transparent image) applied to the faces would add some details:

As you can see, the cube went a long way from a boring flat looking thing to this old wood crate. BTW for game asset, don't use textures map which are too big and ideally RE-USE your textures multiple times, by combining them. But this is another story.