So when you're in a climbing gym you're going to see lots of tape spread out all over the walls. All those pieces of tape are marking specific climbs, and those specific climbs are designed to start at the bottom of the wall and extend all the way to the top. The grading is different for whether or not you're climbing a route or a boulder problem.
There are two scales that you'll typically find in climbing gyms. When you're bouldering most boulder problems are going to have what's known as a V-grade. The V stands for Vermin. John the Verm Sherman is the gentleman who invented that systtem. Started down in Waco, Texas. There's a big bouldering area there called the Waco Tanks which kind of gave birth to the V-scale as it's known.
Bouldering grades begin at V0 and go all the way up to about V15 or V16 right now. Pretty substantial difference in the way each boulder problem progresses and the difficulties between a V1 and a V2, and a V2 and a V3. Also very subjective when you're dealing with how to grade a boulder problem. Everybody climbs differently, lots of different body types, lots of different route setters.
So, although the grades should give you a pretty good idea about which climbs are harder than others, don't ever be deterred about falling on a certain climb and then trying something harder because you fell on an easy one. Try all of them, and try everything that looks fun. Don't be deterred by the grades. Just use them as a guide.
When you're climbing routes the scale differs. Instead of seeing a V you're going to see a 5 point something. Normally in climbing gyms the 5.4 or 5.3 will be an intermediate or beginner level climb. Now that's kind of where the grading starts. This system is known as the Yosemite decimal system. It started in Yosemite, California.
So, moving from 5.3 up to about 5.9 is where you'll have just a single number - 5.3, 5.4, 5.5, up to 5.9. Right around 5.10 climbs start to often integrate a letter as well. So you would have 5.10A, B, C, and D meaning that there are some subtle differences in whether or not it's an easier 5.10 or maybe a more challenging 5.10.
Continuing on up the spectrum those numbers would go up to 5.15. Right now I think some of the hardest climbs established are around 5.15 B, maybe 5.15 C, but that's all happening, for the most part, outside. In the climbing gym you won't see much above 5.13. So really aim for the 5.3 to 5.6 as kind of your beginner level climbs, 5.7 to 5.9 would be an intermediate level, 5.10 and up is going to be pretty advanced.
But, once again, try everything that looks fun. Don't hesitate to try a harder climb if you just fell on something easier. And all those pieces of tape that are on the wall are marking those specific routes for those specific grades. So following a single color is where that difficulty is going to come into play.
That's how to understand climbing grades and a bit about the taping.