To be successful in finding and catching Shinies, it's essential that you properly prepare. Here's what you'll need:

The Poke Radar

Where to get it: Once you have completed the Sinnoh Pokedex, you can obtain the Poke Radar from Professor Rowan in Sandgem Town.
What it does: The Poke Radar is a tool that helps you find non-Sinnoh Pokemon that were previously unattainable in Diamond/Pearl. It can only be used in regular grassy areas (not tall grass), and cannot be used anywhere else - so forget about trying to use it in caves, while surfing, etc. The Poke Radar can also be used to help you increase your odds of catching a Shiny by allowing you to use a technique called "chaining," which basically involves battling the same Pokemon over and over. More on this later.

The Poke Radar Poketch application

Where to get it: Once you've obtained the National Dex, visit Professor Oak at Pal Park and he'll give it to you.
What it does: It helps you keep track of your Poke Radar chains. It shows you your top three highest chains, as well as the current chain you're working on.

Above: Having a Pokemon with the Static ability increases your chances of encountering other electric-type Pokemon, which may help you when chaining for electric-type Shinies

Plenty of Super Repels or Max Repels

In order to use the Poke Radar correctly, you must eliminate the chance of encountering a wild Pokemon in a random battle. You only want to encounter Pokemon that appear as a result of using the Radar, because encountering any other Pokemon will break your chain. To prevent this, you must have a Repel in use at all times. Super Repels are cheaper per step, but if you have money to burn and you would prefer to use Max Repels, that's fine too. 

Supply of Poke Balls

This one is obvious, but make sure you have a good supply of Poke Balls. Make sure they're the appropriate type for catching the Pokemon you're going after. Plenty of Great, Ultra and Dusk Balls never hurt.

A party of able-bodied Pokemon

Before you start, make sure you have Pokemon in your party with tons of PP and strong moves to KO many Pokemon. Once you start your chain, you won't be able to go back to a Poke Center without destroying your hard work, so make sure you have strong Pokemon that can handle many battles without running our of HP/PP. It's also handy to have a Pokemon in your party that knows the move Super Fang or False Swipe so that when you find the Shiny, you won't KO it if it's at a lower level. 

If you're looking for electric-type or steel-type Pokemon, it's also a good idea to have a Pokemon with the ability Static (electric) or Magnet (steel), because it will increase your chances of encountering other Pokemon of that type. Make sure the Pokemon with that ability is in the lead of your party though, or else it won't work.