Banks are easily found in the major centres. Opening hours are generally Monday to Friday, 8.30am to 2.30pm, with some branches open on Saturday from 8.30am to 11am. Most banks and hotels should be prepared to change traveller's cheques, but usually at poor rates of exchange. Most ATMs in Swaziland accept international cards.
Currency is the lilangeni - plural emalangeni (E) - which is tied to the South African rand (1 rand = 1 lilangeni). The rand is legal tender in Swaziland, so you won't have to change any money, but note that emalangeni are not convertible outside Swaziland. There is a shortage of change in Swaziland, so if you do exchange money ask for a good amount of low denomination notes.
Credit cards such as Visa, Mastercard and American Express are widely accepted in hotels, restaurants and shops. The national parks accept cards for larger payments such as accommodation, but you'd be well-advised to carry cash to pay for meals and guided walks.
Costs are similar to those in South Africa, with food and fuel somewhat less expensive.