Sure! Here's a Python script that should accomplish what you're looking for:

```python
import os
import shutil

# define the paths to the desktop and the target folders
desktop_path = os.path.expanduser("~/Desktop")
target_folders = {
    "Documents": ["doc", "docx", "txt", "pdf"],
    "Pictures": ["jpg", "jpeg", "png", "gif"],
    "Videos": ["mp4", "avi", "mkv", "mov"]
}

# loop through all the files on the desktop
for file_name in os.listdir(desktop_path):
    # get the file extension
    extension = file_name.split(".")[-1].lower()

    # find the target folder for this file type
    target_folder = None
    for folder, extensions in target_folders.items():
        if extension in extensions:
            target_folder = folder
            break

    # if we found a target folder, move the file to it
    if target_folder:
        source_path = os.path.join(desktop_path, file_name)
        target_path = os.path.join(os.path.expanduser("~/"), target_folder, file_name)
        shutil.move(source_path, target_path)
```

Here's how the script works:

1. The `desktop_path` variable is set to the path to the user's desktop directory.
2. The `target_folders` dictionary maps each target folder name to a list of file extensions that should be moved to that folder.
3. The script loops through all the files in the user's desktop directory using `os.listdir(desktop_path)`.
4. For each file, the script gets the file extension using `split(".")[-1].lower()`.
5. The script then loops through the `target_folders` dictionary and checks if the file extension matches any of the extensions for a given target folder.
6. If a target folder is found, the script constructs the source and target file paths using `os.path.join()` and moves the file to the target folder using `shutil.move()`.

Note that this script assumes that the target folders already exist in the user's home directory. If they don't exist, you'll need to create them manually before running the script. Also, be sure to test the script on a test directory before running it on your actual desktop!
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