First and most important, make sure you have a supply of thin rosin core solder. Do NOT use acid-core solder, that is for plumbing.
If you are replacing jacks and not plugs, first try cleaning them. Sometimes that is all that is needed. I just roll up a small piece of 180 grit sandpaper so it can be "plugged into" the jack and rotate it while moving it back and forth. Won't take much of that to remove corrosion. Others prefer to use Caig De-Oxit and you can't go wrong with that either, just make sure you have adequate ventilation.
A system for stabilizing your components while soldering is worth it's weight in gold. I use an X-acto with 2 alligator clips, like this one - http://xacto.com/products/cutting-solutions/tools-accessories/detail/X75140
It works well and has saved me a ton of frustration.
Surf the web for information on "tinning" the tip of your new soldering iron. This will be an opportunity to adjust the temperature. If your kit included a sponge to wipe the tip of your soldering iron be sure to keep it moist when using it and quickly wipe the tip. Otherwise you will burn something stinky, not nice!
Are you soldering the cables to jacks or to plugs?
For best results, carefully dress the leads on your cable, make sure to match to wiring on both ends! There are 2 common types of 1/4" cabling for studio - TS = Tip (positive or +) Sleeve (ground or -) and TRS = Tip (+ signal) Ring (- signal) and Sleeve (ground -).
I would highly recoomend using Switchcraft plugs and jacks, they've been an industry standard for a LONG time with good reason. Ma Bell used them in patch bays for phone systems, during WWII the Military used them for communications equipment, virtually all US guitar companies (Fender, Gibson, Gretsch, Guild, even inexpensive Silvertone Danelectro) used them well into the 1970s. There are other good options but Switchcraft has worked well for me for a long time, every guitar I own has been retro-fitted if it doesn't have one.
They are durable and easy to solder, they can take a lot of heat!
If you are unsoldering and replacing then the leads should be dressed to correct lengths and tinned already.
If any of your cords are of questionable quality in any respect, toss them and get some quality cable (Belden is one good brand) and make your own custom length cables.
Dress your leads, remove a small amount of insulation and tin the multi-strand wire (solid core wire is not the best choice for audio cables).
Next, tin the area you are going to solder the wire to, if you have everything clamped and ready to go keep the soldering iron on the area you've just tinned, slip the wire into the hole and allow the tinning on both parts to melt together. You may need to add a small amount of solder to get that to happen. When there is a shiny, single, small blob of melted solder, carefully remove the iron. You do not want anything to move while it cools, this is why the X-Acto "extra hands" or something like it are needed. Once it's cooled it should still be shiny and smooth.
That will be a reliable solder joint.
It is a good idea to practice first and get good at it. Soldering is cables is really simple if you use the correct procedures.
Circuit boards are another matter entirely, don't assume what you do with cables will be best practice for that.
You'v reminded me that I need to go through all of the cables in my studio rack that are too long and re-work/replace them with custom lengths. Cheers, Kuru