A current is nothing but charge on the move, so a wire in a magnetic field feels the same push a single charge would — added up over every carrier in it. That sum comes out beautifully simple: $F = B I L \sin\theta$, read aloud F equals B I L sine theta. $F$ is the force on the wire in newtons, $B$ is the field in tesla, $I$ is the current in amperes, $L$ is the length of wire actually INSIDE the field in metres, and $\theta$ is the angle between the wire and the field. This is the motor effect, and it is the reason every motor on your site turns. Here $F$ is always the unknown; everything else arrives on the drawing.

Now put a second wire beside the first. Each one makes its own field, each one sits in the other's, and they push on one another: $F = \dfrac{\mu_0 I_1 I_2 \ell}{2\pi d}$. The subscripts label the two wires — $I_1$ is the current in the first, $I_2$ in the second, both in amperes, and which you call which makes no difference. $\ell$ is the length of the parallel run in metres, $d$ is the separation between the wires in metres, and $\mu_0$ — mu-nought — is the permeability of free space, $4\pi\times 10^{-7}\ \mathrm{T\cdot m/A}$. Note that $d$ is not squared: this is an inverse FIRST power, because a long straight wire's field spreads out over a cylinder rather than a sphere.

The direction is easy to remember and worth remembering: currents running the SAME way attract, opposite ways repel — the exact opposite of what charges do. And this relation used to define the ampere outright: two infinite parallel wires one metre apart carrying one amp each trade $2\times 10^{-7}$ newtons per metre. That is a tiny force between two wires and an enormous one between two busbars in a fault, which is why switchgear bracing is not decorative.