A proper frame-rate independent newtonian physics integration:
Vector forces = 0.0f;
// gravity
forces += down * m_gravityConstant; // 9.8m/s/s on earth
// left/right movement
forces += right * m_movementConstant * controlInput; // where input is scaled -1..1
// add other forces in for taste - usual suspects include air resistence
// proportional to the square of velocity, against the direction of movement.
// this has the effect of capping max speed.
Vector acceleration = forces / m_massConstant;
m_velocity += acceleration * timeStep;
m_position += velocity * timeStep;
Tweak gravityConstant, movementConstant and massConstant until it feels right. It is an intuitive thing and can take a while to get feeling great.
It's easy to extend the forces vector to add new gameplay - for instance add a force away from any nearby explosion, or towards black holes.