I've seen advice here for resizing, which is fine if you have another linux distribution to work with.
How can I do resize the partition otherwise? Are there any Windows tools for example?
You can then use
resize2fs as described in the linked wiki page.
I have not been able to resize the image on the SD card directly under Windows, however you can back up the linux partition to a file (as described in another question), run
resize2fs on the file, then restore the enlarged partition from the file back to the partition on the SD card.
The easiest thing is to image the OS onto a SD card.
Then using MiniTool Partition Wizard you can very easily change the size of partitions on the SD card.
There is also an option in raspi-config that will set the OS to use the whole of the SD card, if that's what your after