Commuting in Reykjavik, Iceland can be relatively easy due to the city's relatively compact size and efficient public transportation system. Cycling and walking are popular options for shorter distances and there is an extensive network of cycling paths all around the metropolitan area. Driving into Reykjavik city center from the suburbs in the morning and back in the late afternoon can sometimes be challenging due to heavy traffic.
The bus network is extensive, and it is relatively easy to figure out. The bus transportation system in Iceland is called Strætó. The website for the bus company serving the Reykjavik metropolitan area publishes bus routes, timetables, connections and price-plans: https://straeto.is/en. The most convenient way to buy tickets is to use a dedicated mobile app called Klapp and the app also shows real-time information about the location of the nearest bus and can be used to plan bus trips from any address to another address within in advance.
Taxis are found around the city and can be hailed by phone or mobile app. The largest taxi company has a website with information about phone numbers and how to download the mobile app: https://www.hreyfill.is/en/.
It is also relatively easy to rent a car, although the period from May to September can be difficult and expensive as rental cars are in high demand during the peak tourist seasaon. During the winter months some of the local car rental agencies also offer longer-term rental agreements, which are typically for several months at a time and include all maintenance costs and mandatory insurance. Most of the major international car rental brands are represented in Iceland.