Ok, let's say we are standing on a huge inertial frame, a flat 2-dimensional space (just like people living on this planet used to think of the ground they were standing on). Off in the distance ahead of us are 2 train tracks, parallel to each other and separated from each other by a few meters. They are both going off to the east and the west from us, the viewer (using east & west directions assumes we are looking north). And our line-of-sight to them is perpendicular to the straight-lines of these tracks, which go off to the right and left for as far as we want. Let's say if we go way up above this scene, the main points of interest are at the vertices of a huge isosceles triangle, but with the base of the triangle at the top and the 2 equal sides going down from there to join at a 90° angle. There is a train on one end of the tracks to the left, sitting there ready to go towards the right. There is a train on the right side of the tracks at that vertex of the triangle, pointed to the left ready to go. There are clocks at all three vertices of this triangle, as well as people: A clock at the train on the left (call this train A), a clock at the train on the right (call this train B). And we the viewer at the 3rd vertex of the triangle also have a clock. All these clocks are connected to this vast inertial frame we a standing on, and they are all still with respect to the inertial frame and with respect with each other. So they are all synchronized (am I allowed to do that, to synchronize clocks at various points of an inertial frame?). They all show the same time and they are all ticking at the same rate.
Now, people at train A get on their train and start going at a predetermined time (say 10 o'clock AM). Likewise, people at train B get on their train (train B) and start their train engine moving towards train A, also at 10 o'clock. They both are going to increase their speed from a dead stop at exactly the same rate. They will go faster and faster. They will both move at a faster and faster rate, which will start to approach the speed of light. But they will both be moving with respect to their inertial frame at the same rate, only they will be going in opposite directions and on separate tracks. Finally they have their speed up to something like 2/3 of the speed of light (with respect to the inertial frame this is taking place on) and that will be their cruising speed.
Now, according to the special theory of relativity, people in train A will see the clock in train B as going at a slower pace then their own clock, because train B is going at a high speed in relation to train A. Like wise, the people in train B will see the clock in train A as ticking at a slower pace than their own clock. For example, when the clock in train A gets to show 11 AM, they might see the clock in train B as showing 10:50 AM. So they are both barreling along towards each other. Finally they are both approaching the midpoint between where they started from (this will be directly between the left vertex and right vertex of this isosceles triangle, and it will be directly "above" the bottom vertex where us the viewers are watching this from). They put on their brakes at the same time and slow down. Slower and slower and finally come to a stop right next to each other. The people in train A will have been watching the clock in train B tick along slower than their own clock, so once train A has stopped at let's say 12 o'clock their time, they expect the clock on train B to be showing something like 11:30 AM. Likewise, the people on train B have been watching the clock on train A, seeing it ticking at a slower rate than their own clock, so when they stop and get off train B at a point when their own clock says 12 o'clock, they expect the clock in train A to show something like 11:30 AM. Now from the vantage point of us the viewers of these 2 trains from the lower vertex of this huge isosceles triangle, we who are sitting on this huge inertial frame that everything is taking place on, we would have seen both the clock on train A and the clock on train B as ticking at the exact same rate, although they would be ticking slightly slower than our own clock, since they are both moving with respect to us and even some significant fraction of the speed of light. But now everyone is stopped and standing on this one huge inertial frame of reference again. Now, how will the clocks on train A and on train B compare? To us the viewers of these trains, they should both show the same time. To train A occupants, train B's clock should be retarded in relation to their own. To the train B occupants, train A's clock should be retarded in relation to their own. But only one reality will manifest itself once the occupants of train A and train B meet at the middle, correct? What will they see when they view each other's clocks?