How to Teach a Cat to Climb a Ladder
If you want to teach your cat to climb a ladder, put a few of your cat's favorite treats at the top of it to encourage climbing. If the top is too high for you, just choose the highest step you can reach. Tap the top of the ladder to get your cat's notice and call its name at the same time. If your cat pays attention, dangle a piece of string near the first step to encourage your cat to climb up. Keep playing with the string, pulling it up one step higher each time your cat climbs onto a lower step. Once you've done all you can to get your cat interested in the ladder, wait for your cat to decide whether or not it will use it because cats don't take orders from anyone!
Set up the ladder. Presumably, you are not trying to get your cat to climb a ladder so it can help you patch the roof or clean the gutters. Since this exercise is purely theoretical anyways, set the ladder up in a safe place and make sure it is does not reach too high in the air. This will prevent you and the cat from hurting yourselves when trying this out. Cover the ladder in carpet. A cat will be far more likely to climb up a ladder if it can comfortably grip the steps. Since cats use their claws to dig in and gain traction, cover the ladder steps in carpeting or some other soft cloth to help the kitty get its footing. Leave the ladder out. Once you have covered the ladder in cloth, just leave it out. Cats love to investigate objects they are not used to. Ladders only work for one thing, climbing up and down. Just leaving this interesting new thing out for the cat may be enough to get the cat to climb it. A cat that is not forced, watched, or feeling that it is obliged to perform is more likely to discover the ladder and make an ascent for the fun of it, without your interference or coaxing. Climb up the ladder yourself. Cats are curious creatures. Use this curiosity to your benefit. Climb the ladder yourself and see if your cat is interested enough in what you are doing to simply follow you up. Coax the cat up. If your cat doesn't immediately follow you up the ladder, try calling the cat's name and encourage it to climb to the top. This may be enough to get your cat scurrying right up to the top next to you. Help the cat. If the steps above don't work, then manually help your cat climb the ladder. Take its legs (not tightly) and move its legs up the ladder gently, one rung at a time. If your cat struggles at all, stop. This is a really unnatural exercise and no cat should be forced to attempt it. Put the ladder in place. Place the ladder in a safe place in your house, preferably above a soft surface. Make sure the ladder doesn't lead to anything too high to avoid feline and human injuries. It is probably wise to make sure this ladder doesn't lead to any surfaces you'd prefer to keep the cat off, like counters, shelves, or the kitchen table. Again, make sure the ladder is covered in a soft cloth or carpeting so the cat can get adequate traction. Put treats at the top of the ladder. You can climb the ladder yourself. Or, if you're afraid of heights, just put the treats as high as you can reach and tap on the step with the treats on it to encourage the cat to climb up. Use a toy. If your cat likes to play with a particular toy, use that toy to motivate your cat up the ladder. A string will work best for this, as your cat can follow the string up rung by rung. Keep the cat moving after the toy until it has navigated all the rungs and reached the top of the ladder. Tap the top of the ladder. After trying the treats and toys out, try to encourage your cat by tapping the top of the ladder and calling its name. This final nudge of encouragement may be enough to get your cat up the ladder. Try clicker training. Teach your cat to associate a click-clack noise with a tasty treat. Then lure your cat to the first rung on the ladder. Click and reward your when he looks at the rung or puts a paw on it. Gradually, your cat will learn he gets a reward for stepping on the ladder and you can start to progress him upwards. Wait and see. After trying all of these techniques, your cat may come to associate the ladder with a toy or obstacle to be played with. If this is the case, the cat may ascend the ladder on its own without any treats, toys or encouragement from you. Cats are secretive animals. You may want to try setting a camera up around the ladder to see if the cat may be using it when you aren't around. 
Set up the ladder. Cover the ladder in carpet. Leave the ladder out. Climb up the ladder yourself. Coax the cat up. Help the cat. Put the ladder in place. Put treats at the top of the ladder. Use a toy. Tap the top of the ladder. Try clicker training. Wait and see. 