1. Be sure to purchase the correct size wipers. Ensure not only correct length, but also correct attachment.
Your question is not model-specific but I reviewed all the 2003 Jeep models and they all appear to have standard hook arm attahments. See the link below to view installation videos for hook arms.
The 2003-2004 Jeep Grand Cherokee takes 21" replacement windshield wiper blades on both sides front. The front blades are available aftermarket at stores and online. The rear wiper blade is dealer-only.
The 2002 Jeep Liberty rear wiper blade is unique to Jeep. You'll probably have to get the part at the dealer and may be able to ask for the install procedure.
The 1993 Jeep Grand Cherokee takes 20" replacement windshield wiper blades on both sides front and an 11" or 12" rear wiper blade.
The 2009 Jeep Grand Cherokee has standard hook-end wiper attachments on the front and a fairly specialized pinch tab rear wiper arm attachment. See sources and related links below to view wiper blade installation videos and for information on the special rear wiper blade.
The 1994-1998 Jeep Grand Cherokee takes 20" replacement windshield wiper blades on both sides front and an 10" or 11" rear wiper blade.
The 1999-2000 Jeep Grand Cherokee takes 21" replacement windshield wiper blades on both sides front and an 10" or 11" rear wiper blade.
The wiper arm (not the wiper blade) has a u shape bend on the end of the arm. So you have to pull the arm away from the Jeep, then turn the blade a half turn, pivoting it around the end of the arm, then pushing down towards the bottom of the arm.
The 2004 Jeep Liberty has a special Jeep rear wiper blade that you have to go to the dealer for. When purchasing the wiper, ask the dealer for the replacement instructions. There are aftermarket options available for the front however. See sources and related links below.
The 2002 Jeep Liberty takes 19" replacement windshield wiper blades on both sides front.
how to change the windshield wiper motor in a 2000 jeep wrangler
You can try Quadratec.com, Rockauto.com, or your local jeep dealer
The 2007 Jeep Liberty has the most common hook-end wiper arms. See sources and related links below for installation videos. Also, purchase the replacement blades first and there will be additional instructions/illustrations on the replacement packages. Locate and press the tab or button where the wiper blade is inserted into the hook of the wiper arm and pull wiper blade out of hook. You may have to rotate and flex the blade to make enough clearance for the hook to pass through.