You can find Dripstone Blocks in Minecraft by speaking with Mason Villagers who have reached Journeyman levels, or you can find it naturally in caves hanging from the ceiling. If you use a pickax to break them down, you can place them at any location you want. The ones you naturally find have a chance of having Pointed Dripstones hanging from them, which should be dripping water down to the ground, becoming a stalactite. If a Dripstone Block is on the ground, the Pointed Dripstone becomes a stalagmite.
It all comes down to having a water source. When you place a Dripstone Block down and have a water source above it, the block drips water. However, while it has the appearance of dropping water, it won’t have enough to fill a cauldron or anything else. It’s merely an animation. What you need to do is have a Pointed Dripstone on it, and when it’s on the bottom of the block, it’s a stalactite. When a stalactite appears with a water source above the Dripstone Block, the water dripping down will fill cauldrons. The same goes for a stalagmite, but the water source needs to be beneath the Dripstone block.
If you’re waiting for a Pointed Dripstone to grow, you’re going to be waiting for quite a long time. There are 20 game ticks every second in Minecraft, and for every tick, there is a 0.0113 chance of a Pointed Dripstone to grow from a Dripstone Block. That means that, on average, you’re going to be waiting somewhere between five days in your Minecraft game for it to happen. So long as you’re patient, it can happen.
There is no way to influence this in your Minecraft world. You merely have to be patient. If you’re looking to acquire more Pointed Dripstone, alternatively, you can have a Mason Villager trade one emerald for two of them, but there’s a chance a Mason Villager will not have this trade available.