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This is for narrower strips, such as inlay materials. Use a shear. I have one that's made for trimming picture frame mouldings and it will give a cleaner edge than anything else. I resaw my veneer at 3/16" and cut it close on the band saw then use the shear. Before I got this thing I'd cut on the bandsaw and then trim using the 12" disc sander. This works very well, but isn't as efficient.

For wider strips I use a sled on the table saw and a handplane with a shooting board.

If you're using thineer pieces, like 1/16 or smaller, then sandwich them in mdf and cut on the tablesaw or bandsaw using a good blade and good sled.

 

You didn't say how wide or how long. But very simply, I've used a steel rule, like a yardstick. You can get them very long, like 6'. HD has them in aluminum, and they work too. I lay the sheet of veneer flat and tape it down on the edges to mark it off. Then I place a length of masking tape along the top and bottom edge and mark it off for the widths, with a fine mark from a 5mm drawing pencil.

I lay the straightedge on the two marks and using either an X-Acto knife or a sharp utility knife very lightly drag the blade down the edge to start the cut. You don't want too much pressure on the first couple of passes or you may be chasing grain with the knife. After a pass or two, increase the pressure to follow the score you first made. You can get very clean cuts this way.

If your strips are to be matched or are an inlay, you may want to hold the knife on a set angle when cutting to give a slightly beveled cut that can be dressed to fit another mating edge.

There are veneer saws that when used properly can give good results cutting veneer, like this one.

Another saw you might try is this one.
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