November 1, 2014 Rwanda instituted a visa on arrival process for the US and several other countries that had previously been visa-free. Other impacted nationalities are Australia, Germany, Israel, New Zealand, South Africa and the UK. All other nationalities must get visas in advances, except certain African countries, while nationals of Hong Kong, Mauritius, Philippines, and Singapore remain visa-free for stays up to 90 days. See announcement from the Rwandan Embassy in Washington, DC.
Visas are available at all ports of entry and cost US$30. Only single-entry visas are available on arrival. No free transit visas.
Kigali Airport accepts cash or Visa credit cards, subject to a $2 fee that is not disclosed until it is too late to cancel the transaction. At the airport you pay at one desk, collect a receipt and then present that to an immigration officer along with arrival card.
On land borders, at least at the DR Congo border at Gisenyi, it is necessary to go the immigration officer first , then go to a separate window to pay, and then return to the immigration officer with the receipt.
I passed through both this week and the process was smooth.
It is also possible to apply online for the same $30 or to get a visa in advance at a Rwandan diplomatic mission. Multiple-entry visas are $60. See details for US citizens from the Rwandan Embassy in Washington, DC.