One of the nice things about Microsoft products is that they have a lot of prefab goodies. OpenOffice.org is a little more of a from-scratch situation. But you have much more flexibility, and you can still do a lot of great stuff. It's not easy, at least not using this approach, to add borders all around, but you can do it in the top and bottom.
Step 1: Add graphics to the gallery.
You can find lots of great graphics on the Internet by googling for "free clip art." For the purposes of borders, keep an eye out for graphics that are small, i.e. under an inch by an inch, and also that have some white space around them.
Step 2: Learn to use the feature documented here.
I'll also describe it in this blog but that's another one that talks about using it in general. Can't hurt to skim that blog.
Step 3: Use this blog entry to add top and bottom headers and footers with any appropriately sized graphic in your gallery.
NOTE: To take out the repeating background borders in this blog, use the instructions here or just Undo (Ctrl Z or use the Undo icon) to go back to not having a background border.
How to Create Graphical Top and Bottom Borders in the Header and Footer
First, open your document.
You now have headers and footers. The graphics will repeat in the background of each to create the graphical border.
Next, turn on the Gallery by choosing Tools > Gallery or clicking the Gallery icon.
Find a category you like, then find a graphic you want to use. Drag the graphic into the document to see how big it is, if you don't know. This one, for instance, is too big. To delete it, just select it so that the green handles are showing, in the document, and press Delete on your keyboard. You can also press Ctrl Z or use the Undo icon.
This one is better. It's a good size, plus there's some white space around the graphic so that when it tiles, you won't see part of another row of the graphic.
Delete the graphic from the document once you know which one you're going to use.
Right-click on the graphic, in the gallery, and choose Insert > Background > Header.
Click in the header and press Return once or more times to add more space, to show the entire graphic.
If part of the graphic is showing on the right side, click in the header and move your mouse over the ruler, at the edge of the right margin. When your mouse becomes a 2-ended arrow, click and hold down, and drag to the left or right to show the amount of graphic you want.
Then only whole graphics will show.
Then click in the footer, and do the same thing. Insert the same graphic, or another graphic if you want, in the background of the footer, then adjust it as necessary the same way you adjusted the header.
Choose File > Page Preview to see the document.