On manipulators, Direct Kinematics is the group of equations where, based on the motor's positions (the joint positions, normally in radians), you'll find the spacial (normally Cartesian) pose of the end effector.
Inverse Kinematics, on the other hand, is the process to find which joint positions are necessary to have the end effector on a specific pose in space. They can be analytic solutions based on the arm configuration, or (most commonly) numeric ones (for example, using Newton-Raphson approximation), and it's normal to have multiple solutions for the same position. Besides that, you'll probably need to control the velocity and trajectory of each leg using a task space controller or something like that, where you'll have to learn differential inverse kinematics.
On mobile robots with arms, each individual leg can be viewed as a separate manipulator, so you can calculate the position of each individual leg with the inverse kinematics of each one, in relation to their base, in relation to the robot origin.
To make the robot move smoothly, however, as in a trajectory, you'll have to study the specific kinematic chain of the type of robot you're working (or develop one). It's not an easy or trivial task if you plan to do it right.
V-Rep has the option to take care of the dynamics to a certain point and has tools for inverse kinematics.
Here are some links that you may find useful:
Inverse Kinematics module on V-Rep
Inverse Kinematics and Motion Masterclass
Video and tutorial of Creeping Gait IK
Kinematics analysis and simulation of quadruped robot by Ni Meng and Wang Xiaodong (2011).
Quadruped Robot Creeping Gait Stability Analysis and Optimization Using PSO by Firas A.Raheem and Murtadha Khudhair Flayyih (2017).