Well, the first thing you need is a decent rigging diagram for the
Arizona. If you're really serious about it and don't mind spending some money, you can get a fine set of plans from The Floating Drydock. That will tell you all you need to know about the rigging - and just about every other aspect of the ship. On a less ambitious level, several good plans have been published in books. Paul Stilwell's
Battleship Arizona, for instance, has a series of drawings showing the ship's configurations at different dates - including 1941. That drawing, in conjunction with the many excellent photos in the same book, probably would be more than adequate as a guide for rigging a model on 1/350 scale.
Different modelers have different opinions about rigging materials. I've never done a 1/350 model seriously, but I've done lots on 1/700. On that scale I usually use stretched sprue for most of the lines.
If you've never stretched sprue - here's a quick explanation. "Sprue" is the nickname given to the plastic "sticks" to which the parts of a kit are attached. After removing the parts, take a piece of sprue and hold it (with both hands) over a candle. Roll it back and forth, so the heat is distributed fairly evenly around it. After a few seconds the plastic directly over the candle will start to soften. Pull gently with both hands. The sprue will become an extremely thin filament. The faster you pull, the thinner it will get. Before you start rigging the ship, make up a supply of several dozen lengths, in different diameters. For best results, let them cool off overnight.
The next step is to determine the precise length of a particular piece of rigging. To do that, the best tool is a small pair of dividers. Cut the sprue to length.
There are two popular adhesives for sprue rigging. Some people like superglue; my preference is white glue (Elmer's). I like it because it shrinks a little as it dries, and it's water soluble. (If the line ever breaks, it's easy to remove the glue and start over. Just touch it with a brush full of water.)
For handling the lengths of sprue, I like to use a pair of tweezers that are designed for stamp collectors. They have wide, flat tips, like spatulas. Pick up the sprue with the tweezers, dip each end in a drop of Elmer's, and put it into place.
The first dozen or so attempts will give you a headache, but don't despair. There's a short but steep learning curve in rigging. If you can make yourself stick with it for a couple of hours, you'll find it's getting easy.
For longer pieces, I recommend using fine wire. I personally use a spool of nickel-chromium wire that a friend found years ago at a military surplus store, but fine copper wire works fine. A good source is Radio Shack. Buy a spool of the finest multi-strand electrical wire they have, strip off the insulation, and untwist the individual strands. Or buy a cheap pair of stereo earphones for a walkman and cannibalize the cord. You can find some incredibly fine wire that way.
When the rigging is in place, and the glue's dry, paint the rigging with thin paint of an appropriate color (probably dark grey). This is an important step. Unpainted sprue is shiny, and the shininess has the effect of making it look thicker. The glue holding the rigging in place will show up as shiny dots. A drop of paint in the appropriate color will make them disappear.
Each piece of rigging presents its own problems, but the above should give you the general idea. Good luck.