Buy some. The best "replacement" for not having Fudge dice is to buy some! Grey Ghost Press (maker of Fudge) sells a tube of four Fudge dice for about 5 bucks, or a bag of twenty Fudge dice for about 15 bucks, but a lot of places are sold out. However, Indie Press Revolution just started carrying Fudge Dice (four or twenty) to support the FATE-based games they're selling, such as the Dresden Files RPG.
Make some. A Fudge die is just a six-sided die with three different values: a plus ('+') on two faces, a minus ('-') on two faces, and the other two sides blank. Either buy some blank dice or take a marker to some pipped d6es.
There's an app for that. There is more than one Fudge die roller on the internet. Gordon A. Cooper's roller is simple and easy to use. Also, because a single Fudge die is equivalent to 1d3-2, any dice roller that can roll 4d3-8 can give you a perfect 4dF roll. MachDice for the iPhone will roll Fudge dice without playing with 4d3-8 expressions. On the Droid smartphone platform, DroidDice and Dice & Roll Lite will let you put in a 4d3-8 expression and name it "Fudge" for convenience.
Make do with d6es. If you want a perfect 4dF distribution and don't want to take a marker to your dice, you can roll 4d6 and treat all 1's and 2's as a -1, treat all 3's and 4's as a +0, and treat all 5's and 6's as a +1.
Cheat a little. Some FATE-based games are doing a d6-d6 roll. That is, use two different d6es, specify which one will be the minuend and which will be the subtrahend, and then the result is the difference. This produces a number between -5 (1 minus 6) and +5 (6 minus 1). You can use dice of two different colors ("the green one minus the red one") but I like to use a big die and a little die ("the big one minus the little one").
Pick a card, any card. Remove one suit and the jokers from a deck of playing cards. Assign each of the remaining suits to the +1, 0, -1 die results, then draw four cards. If you remove the Clubs, then this device will help you remember which suits are what values: Spades point up, so +1. Hearts point down, so -1. Diamonds don't point anywhere, so those are 0.
Cards can be a bit of a pain in the ass because you have to keep shuffling your draw cards back into the deck, else you mess with the probabilities. However, it's great for car trips and hikes and those days when you left your dice at home and would rather play The Shadow of Yesterday or Starblazer Adventures than poker. You can even use tarot cards.
Simulate it with percentiles. Any dice mechanism with a known probability table can be simulated with a d100 or d1000 or the like. The d1000 will be more accurate, if you care about such things; I rounded a bit here and there, generally in the player's favor.
d100 d1000 Fudge Result
------- --------- ------------
01 001 - 012 -4
02 - 06 013 - 049 -3
07 - 19 050 - 185 -2
20 - 38 186 - 383 -1
39 - 61 384 - 617 0
62 - 81 618 - 815 +1
82 - 94 816 - 938 +2
95 - 99 939 - 988 +3
00 989 - 000 +4
There are many choices, and not all of them produce the same results statistically. Check out the FATEwiki's entry on Fudge dice for probability tables for different randomization methods.