If you're having trouble deciding what type of guitar strings to put on your beloved axe, fear not! Once you get a few fundamentals out of the way, your choice will mostly come down to playing style and personal preference.
First, you need to determine what type of guitar you have - acoustic nylon, acoustic steel string, or electric. You want to be sure to use the correct strings for your particular guitar. Acoustic guitars that require nylon strings, such as classical, flamenco and some folk guitars, generally have lighter tops, or soundboards, with less internal bracing than those found on steel-string acoustics, and stand the risk of serious damage if fitted with steel strings. Steel-string acoustics are designed to withstand the added stress that steel strings exert on the top, bridge, nut and neck, and won't sound very good with nylon strings, if they even fit. Electric guitar strings must be made of ferromagnetic metals like steel and nickel, so they can interact with the magnetic pickups, while acoustic-electric guitars typically use a different type of pickup which senses vibrations from the bridge, so acoustic strings may just have a steel core wound with a phosphor bronze alloy wrap for bright tone. Guitars with whammy bars might require a few extra steps to keep everything stable, so check your manufacturer's instructions or look for online videos.
The next step is to figure out what gauge, or thickness of string is best suited to your playing ability and style. Thinner gauges are easier to fret and bend, and may be better suited for beginners, until callouses build up on the fingertips. Heavier strings tend to produce greater volume and fuller tone. Nylon strings are typically categorized as light, medium or heavy tension. Steel strings for both electric and acoustic guitars are categorized by the gauge, or thickness of the lightest string, the high E string, measured in thousandths of an inch, with .09 being a common size for an electric set. A set of electric strings may be labeled .09-.042 - this is the gauge of the lightest and heaviest string in the set. Acoustic sets are a little thicker, so a typical medium-gauge set might be .012-.054.
Another factor to consider are the alloys used to make the string. Acoustic strings may be phosphor bronze or an 80/20 bronze/zinc alloy, electric strings may be pure steel or a steel/nickel alloy, and the outer winding on the thicker strings may be either round wound or flat wound, which is typically used by jazz guitarists for smooth fingering with less fretting noise. Acoustic and electric strings are both now available with special super-thin coatings to protect them from sweat and corrosion. Coated strings cost more, but generally last much longer. Find out what type of string your favorite player uses, try guitars with different types of strings at your local guitar store, then try a few different sets on your guitar to see what feels and sounds best for your playing style. Major manufacturers include Ernie Ball, Martin, GHS, D'Addario, and Elixir, among others. Make sure you have a string winder to make installing the strings go faster, and some pliers with a fine wire cutter to clip the excess string from the tuning post, a well as some guitar polish - changing strings is a good time to perform some routine maintenance. Keep a clean cloth in your case to wipe down the strings after each use, along with extra bridge pins for your acoustic guitar. Regular string changes are the best way to keep your tone crisp and clear, so grab a pack and tune 'em up!