Roads in northern Kenya
A good network of scheduled and charter flights connects Nairobi to other major cities in Kenya, for instance Mombasa, Malindi and Kisumu, and light aircraft flights connect and all the main game reserves to Nairobi and to each other. Not that most but not all domestic flights to/from Nairobi depart and arrive nor from Jomo Kenyatta Airport but from the smaller Wilson Airport (WIL), so check your booking.
Most people explore the country on an organised group or bespoke safari or tour, which can be arranged through innumerable international and local operators.
Most trunk roads are all surfaced and well maintained, so self-drive is an option, provided you have a valid license, but be aware that driving tends to be reckless by Western standards. Driving is on the left side of the road, as in the UK, which may require some adjustment for drivers accustomed to driving on the right.
National parks and other safari destinations are not generally accessible on public transport, but it is easy enough to travel between towns by bus or local matatu minibuses. Be warned that these are often poorly maintained, overcrowded and recklessly driven, and fatal accidents are commonplace. A notable exception is the historic train service that connects Nairobi to Mombasa, a trip that qualifies as an attraction in its own right.