With a vehicle with steered wheels the simple approach is to calculate the centre of rotation for the vehicle and then, given the speed of the vehicle, the distance travelled around the arc can be calculated. This results in a change in position and heading.
The centre of rotation can be determined by projecting lines along the axles of the four wheels and finding where they intersect. Normally the rear wheels are non steering so they project a line along the rear axle line. If the steering geometry is 100% Ackermann, the lines projected from the front axles will intersect at the same point on the rear axle line, giving the centre of rotation.
The 'AckerMann Steering Geometry' and 'Slip Angle' entries on Wikipedia cover this quite nicely without getting bogged down in the maths.
Note that this is a simple model which ignores wheel slip, static toe etc
A slightly more complex approach is to calculate the angle of the wheels relative to the motion of the vehicle (aka the slip angle) and then determine the force vector generated by each wheel.
Each wheel has a longitudinal force (rolling resistance and driving/braking torque) and a lateral force (generated by the slip) which combine to give the force vector.
Each of these forces act upon the vehicle to give a net acceleration (both linear and rotational)
This approach requires knowledge of the wheel loads and, at the least, an estimation of the tyre slip-force curves, although you could assume the force is linearly dependent on slip angle for low speed modelling.
If you want to really simplify matters you can treat the vehicle as a bicycle model i.e. two wheels on the centreline, one steering.
The position calculation can then be approximated by using the steering angle to generate a rotation around the centre of gravity (the steering angle is roughly proportional to a force which acts along the axle line of the wheel) and then travel in a straight line using the vehicle velocity over the sampling interval. In some regards this is similar to the calculations required for a tracked vehicle.