I was reading that if we travel closer to the speed of light ( let us say we are going at 270,000,000 m/s ), time slows down. [ I didnt provide references cause it seems to be a well known fact. ]
In that case, what opposite thing/act needs to be done in order to speed up time? Does somehow going farther away from the speed of light, speed up time?
How would we define the speed/action that needs to be done, where time actually speeds up? Is there a term in Physics for that speed/ action?
Your question is based on at least three misconceptions.
Firstly, all motion is relative. You are already travelling at close to the speed of light relative to passing muons.
Secondly, in special relativity time does not 'slow down' in the way you suppose. The elapsed time between two events in one frame can be more or less than the elapsed time in another. However, a second is a second in any given reference frame.
Thirdly, it makes no sense to talk about 'going farthest' from the speed of light. The speed of light is always the same relative to everything, so no matter how you move you cannot move away from light faster than c. The smallest relative speed you can have is 0m/s. A negative speed is not smaller than zero speed- the minus sign just signifies speed in a reverse direction.
I always like to think of an unstable particle when I think about time dilation. For example, when it's outside of an atomic nucleus, a neutron will decay in roughly 15 minutes. Let's say you made a device that produces a beam of free neutrons with speed $v$ and measured the time it took for a single neutron in the beam to decay. The decay time you will measure is $$ \Delta t'=\gamma\Delta t. $$ $\Delta t'$ is the time for a process to occur in your laboratory - from the neutron's perspective, it's stationary and your lab is moving around the particle. By contrast, $\Delta t$ is the time it takes for the process to occur in the rest frame of the neutron, in this case, 15 minutes. To determine the time you actually measure for the decay of the neutron, you have to compute the Lorentz factor $$ \gamma=\frac{1}{\sqrt{1-\frac{|v|^2}{c^2}}} $$ of the neutron. Here $c$ is the speed of light and $\vec{v}$ is the velocity of the neutron. $|v|$ is the speed of the neutron - thanks to the absolute value sign, it's always a positive number.
Now we get to your question. For a neutron travelling 90% the speed of light, $\gamma$ is about 2.29. So in your laboratory, you would measure a neutron lifetime of around 35 minutes. If we instead calculated the speed of a neutron travelling at 99% the speed of light, $\gamma$ is roughly 7.1 and $\Delta t'$ is 107 minutes. The time to decay measured in the frame comoving with the neutron doesn't change but the same process is measured to take a longer time by an observer not moving with the neutron. In that sense, if we wanted to "speed up" time, we should decrease our speed relative to whatever we're interested in, as you guessed.
