So far this is what I've got: http://www.limokon.com/junk/hello.html

My problem is the size of the image. Now a days I realize that most people have fast connections, so loading a big image isn't a problem. However, there are a few people who are still on dial-up, and for those people to try to access a website with an image as big as the above, would be horrible. Loading time would take forever if it would even load properly in the end.

SO, I'm asking what to do. Back in the day (that's a few years ago, before I took a 2~3year long hiatus) I would slice the image and use tables to position the pieces together.
However I realize that tables got outdated long ago, so.. now I'm asking, what should I do with my big image??

DON'T use tables, use CSS.

I really don't understand your question though.. the image you posted isn't very descriptive. I'm guessing it is your website layout?

Ah yeah, sorry sort of failed to clarify that...
It's the background image (gonna be for my blog).

Would it be ok to slice the image and use css to position it?

if it's your website layout, then, yeah slicing it might make your images load faster but still..too many slices would cause to call the server many times everytime someone browse on your site, so u have to control your number of slices.

That image is only 134KB, not all that big, even for a dial-up connection. You might be able to optimize a bit more to bring the size down a bit more. Slicing it into pieces wouldn't save you much, and would likely ruin the effect.