So you wonder what it's like on the inside? How does it feel to move through time and space? Quite simply put it's hard to put into words. Your entire body is engulfed in flame your senses are on fire and yet you do not burn. Then as you're in this raging inferno you shotgun yourself in pieces to your destination landing in various places and times and waiting to coalesce as the pieces slowly fall into place and find each other grouping around a focal point. It's a violent process to say the least.
Though that's not to say that it's entirely unpleasant after a while. Granted being ripped apart in such a way is beyond excruciating every time, but coming back together does have quite a euphoric feeling to it. I still wouldn't recommend it on that alone though.
Interestingly stopping time rather than moving through it, or more accurately removing yourself from time is actually a very chilling and cold experience. Chilling in the frightening way as you feel the sudden disconnect from everything and you know you're all alone. During this you're also experiencing a cold snap making it difficult to function as you'd rather go skinny dipping in alaska than spend any more time where you are. Thankfully that feeling passes relatively quick.
There's not much I can think of to say about it beyond that. After your movements are complete it's basically business as usual. Returning to the present from the past or future is the same process however returning from stopped time is more like watching reality fade in. You see the shadows and ghosts of things slowly coming back into existence as you rejoin the timeline and once everything appears to be solid it just seems to pop into motion all at once. I may even be mistaken but it seems like after returning time moves a little faster for a while, almost as if to catch up for time lost.
It's worth mentioning that your clothes don't really like time travel usually. I often find they don't hold up well and come out with holes in them or slight burns. It's possible these parts simply haven't coalesced yet but it's not such a big deal, at least they're not fusing with the body. This comes aside from the fact they stand out in the past and future because they're clearly from the wrong time period. Often when traveling you have to pick up new threads wherever you land, frequently stopping time in order to do so without drawing attention. It's for this reason I often do my time traveling with minimal clothing. I tried bringing a bag of appropriate clothes with me once, they got lost in transit.
Hopefully this is of some use to you fellow time travelers at some point.