You should take photos of the basement and water coming down the stairs.
You should keep all receipts for any repairs or cleaning you had to do due to the flooding.
You should prepare a letter and send to your neighbor informing him that his/her recent landscaping has resulting in flooding of your yard and demanding that he correct the condition.
If the neighbor does not voluntarily agree to address the condition, you will need a local real estate attorney with litigation experience to represent you. The condition is a nuisance within the meaning of the law.
If this answer was helpful, please mark it as helpful or as a best answer. This answer is for general education purposes only. It neither creates an attorney-client relationship nor provides legal guidance or advice. The answer is based on the limited information provided and the answer might be different had additional information been provided. You should consult an attorney.
You should immediately send your neighbor a letter by regular and certified mail which: (a) describes the situation and what happened after your neighbor did the landscaping; (b) demands that he/she remedy the issue; and (c) states that if the issue is not immediately remedied, you will seek to hold him/her liable for all damages incurred by you due to the water flowing from his/her yard into your yard and your basement. If possible, the next time there is a heavy rain, take a video of the water flowing from your neighbor's yard into your own. Take photos of any damage that occurs, and keep all receipts from repair / clean-up work that has to be done due to the flooding. Also, keep a log of every time your yard/basement floods, the time of day it happened, the damage that occurred, etc.
Finally, consult an attorney who does real estate litigation if the situation is not promptly fixed by your neighbor to your satisfaction.