If you are travelling by your own car then it is wise to carry a GPS. Plan your route before start of journey. Although many streets, roads and landmarks are marked in both Arabic & English yet there are few important major streets, roads and exits that are still marked in Arabic only.
It is important to carry your Valid Identification (i.e. Passport / National ID / Iqama) at all the times. You may experience difficulties obtaining accommodation and may experience bigger problems if you are stopped at any of the city's check points (these can be both permanent or temporary). Not being able to show valid identification when asked by the police may land you in jail. Therefore, it is also advisable to keep details of your sponsor on hand in case you require assistance while out and about.
Most visitors rely on white taxis, which are abundant in the city centre but can be harder to find on the outskirts or at night. Drivers will usually use the meter without asking if you do not propose a fixed price, and with a starting fare of SR 5 and the meter ticking up SR 1.60/km after the first kilometer, most metered trips within the city cost under SR 30. However, locals usually prefer to negotiate fares in advance, and this can often be cheaper than using the meter: short hops start at SR 10, a longer journey might be SR 15.
Single women are legally allowed to take registered public taxis, but many female visitors and expats choose not to, opting for transport provided by a hotel, their company or compound instead.
The level of English spoken varies from decent (esp. Indian and Pakistani drivers) to non-existent, so try to find out the name of your destination in Arabic before you head off. Solo male travelers are expected to hop into the front seat, next to the driver, while women must sit in the back.
Drivers are usually familiar with major local landmarks, but you're expected to know your way to your destination from there. Bring a map and the phone number of someone at your destination to call for directions.
Flat-fare minibuses (SR 3) rumble the streets of Riyadh, but these are mostly used by laborers. They are quite difficult for the casual visitor to use: there are no posted stops, and routes are usually written only in Arabic. Most routes converge on al-Bathaa, and the adventurous visitor can try his luck on route 9, which runs from al-Bathaa up Olaya Road.
The best option for traveling in Riyadh is your own car, ideally driven by somebody else used to the conditions, but many expats take the plunge and drive themselves. The traffic in Riyadh is, by Saudi standards, fairly sane: ubiquitous raised bumps on lane markers keep cars traveling more or less in straight line, and radar-equipped cops on the major highways zap the craziest of speeders. Still, the local driving style can charitably be described as "aggressive", with swerving from the leftmost lane to the exit ramp on a four-lane highway being par for course, and central Riyadh jams up almost daily during rush hour.
Since June 24/2018, women are allowed to drive. If you are visiting the Kingdon you can use your international driver license.
The modern, northern half of Riyadh is very pedestrian-hostile, with 8-laned roads filled with speeding SUVs making crossing the road a dangerous exercise. Pedestrian bridges are very few and even at stoplights you need to keep an eye out for crazy drivers. Add in the fearsome summer heat, and it's little surprise that there aren't too many people walking about. In al-Bathaa, though, the situation is almost reversed: some of the alleys are too narrow or congested for cars, and walking is the only way of getting around.
But if you're the fearless type, walking along even the wider roads is a great way to see the city, as you'll be too distracted by constant near-misses while riding in a taxi. Stay in the shade, be careful along stretches without a pedestrian walkway (or one that is blocked off due to construction going on), and you'll be fine.