The solution to such problems is a very simple application of conservation laws. The two relevant laws are conservation of angular momentum, which says that for a particular orbit $$ L = mrv_{\rm tan} = {\rm constant}\ ,$$ where $m$ is the mass of the orbiting body (assumed $\ll$ the mass $M$ of the body it orbits) and $v_{\rm tan}$ is the tangential velocity component (i.e. that component perpendicular to a line between the central mass and the orbiting object) and $r$ is the distance between the orbiting object and central mass.
The second is conservation of energy which says $$ \frac{1}{2}mv^2 - \frac{GMm}{r} = {\rm constant}\ ,$$ where $v$ is the speed in the orbit, which is formed from a tangential component (discussed above) and a radial component directed along a line towards or way from the central object.
In an elliptical orbit and object in general has both a tangential and radial velocity component, except at aphelion and perihelion when the radial component is zero and $v = v_{\rm tan}$.
Thus if we know the speed at perihelion, we can use conservation of angular momentum to work out the tangential velocity at any other position in the orbit and we can use conservation of energy to calculate the speed at any other position in the orbit.
If we are in possession of the speed and one of its components, then we know which way the velocity is directed.