For automatic Dirty Water processing you need to set fluid filters in a Fluid Tank. A Dirty Water Bucket is required to do so. Getting the first Dirty Water Bucket is currently a little tricky. You can do the following steps to get a Dirty Water Bucket and to setup a closed fluid loop.
For this tutorial you need a Wrench and some building materials.
1. Prepare the water source
Build Materials
2 Water Buckets
Drain
Fluid Pipe (Iron, Gold)
Solid building blocks (e.g. Cobble Stone)
Create an infinite water source (2x2 water blocks). Dump the first Water Bucket in the top left corner and the second one in the bottom right corner. Place a Drain (White block with 9 "holes", not to be confused with the Fluid Drainer) below any water source block (It will immediately start to extract water). Afterwards you should place fluid pipes which are connected to the Drain and configure the first pipe to the Extraction type. That can be done with a wrench by selecting a block face with the left mouse button and by changing the pipe mode with the right mouse button.
2. Insert some Water into a machine
Build Materials
A Water consuming machine which also produces Dirty Water:
Advanced Pulverizer or
Advanced Crusher
Fluid Pipe (Iron, Gold)
Solid building blocks (e.g. Cobble Stone)
You need to fill up the Water tank (at least 2.00k mB). Afterwards you should disconnect the water pipe, because Water will be converted to Dirty Water as a by-product.
3. Process items in the machine
Now you should keep processing items until the Water Tank is empty and the Dirty Water tank has at least (2.00k mB).
4. Extract Dirty Water
Now you can place a pipe in extraction mode next to the block - not on the same side as the other pipe - and pump the Dirty Water into a fluid tank.
5. Getting a Dirty Water Bucket
Now you can place another pipe in extraction mode next to the fluid tank and pump the Dirty Water into a Fluid Filler. There you can insert an empty bucket which will produce a Dirty Water Bucket.
6. Setting the Fluid Filter and processing Dirty Water
With the Dirty Water Bucket you can set the Filter in the Fluid Tank. Afterwards you can break the Fluid Filler and replace it with a Filtration Plant block. The Filtration Plant can convert Dirty Water back to normal Water (The Filtration Plant requires Charcoal Filters to do so).
7. Closing the fluid loop
Now you can place another Tank and set the Filter to Water before you connect the pipes.
8. Jump-starting the fluid loop
Now you can connect the Infinite Water source back to the Advanced Filtration Plant. If the Water tank is full, you can disconnect the Water supply again. The system is now a closed loop - the infinite Water source is no longer required. If you'd like to build another processing loop you should keep the Dirty Water Bucket to set the filter of the Tank.