R&R of a radiator on a '99 LHS is a bit labor intensive. First of all, are you sure you need to pull the radiator? If so, then here goes.
First of all, drain the coolant from the radiator. Get under the front end of the car on the passenger side and locate the coolant drain valve. (this is easier if the car is on ramps or on a lift. I would not advise jacking the car up unless you have good trustworthy jack stands to support the vehicle while you are under it.) Open the drain valve and place a drain pan under it to catch the coolant.
Now, open the hood and locate the upper radiator support bracket. The bracket extends from the right fender to the left fender and has alot of bolts holding it on. It also supports the headlamp assembly and also fastens to the front facia with three fasteners. The bracket also usually has all your belt routing stickers and emissions stickers attached. Remove all the bolts from the upper radiator support bracket and remove it from the vehicle. You will notice the hood release cable also fastens on the front of the bracket, once you have the bracket loose, you will just remove the cable from the hood release.
Now you need to remove the electric cooling fan shroud assembly. It is held on by clips and screws at all four corners. You will need to remove these in order to remove the assembly. Also, locate the electrical connector that supplies power to the fans and disconnect it as well. Then, remove the fan assembly from the radiator. Then remove the upper and lower radiator hoses from the radiator. Remove the transmission cooler lines from the radiator as well and wrap some plastic sandwich bag around the ends and tape or use a rubber band to secure the plastic. This keeps the fluid in the lines from running all over the place and keeps dirt/coolant/whatever from getting in the lines.
You will need to remove the coolant hose connected to your reservoir tank as well and secure it with a clamp or something to keep all the coolant from running out of the tank.
Next, check the radiator for any other fasteners, etc. You should be ready to lift it out of the car. Once out, do what you need to do and the installation is the reverse of removal.
Once you put the radiator in and EVERYTHING is back in its place, fill the radiator using the coolant reservoir. (make sure your drain valve on the radiator is closed!) You will notice a small bleeder port on the upper radiator hose housing on the engine. You will need to open this during the fill process to allow air to escape from the system. Once you see coolant flowing from the port and no more air bubbles, close the port. Run engine, check for leaks, continue to add coolant until car reaches operating temp then watch coolant level to make sure reservoir stays on the "full hot" line. Shut off the car and let it cool (usually overnite) then recheck everything in the morning including coolant level, add if necessary.
Good luck! Try to pick up a "Haynes" repair book (autozone) as it will help you alot in this process. The Chilton books are great to use too, however they are usually more expensive and I have made ALOT of repairs using Haynes manuals with great success.