This is looking at the end of the tail stock. Notice the vernier scale. The tail stock is adjustable in case you need to turn a slight taper. I say slight because this doesn't adjust very far.

Also notice the triangle shaped bedways (arrows). This is what the tail stock and carriage ride on, keeping them both moving in a straight line. And as you can see, those areas are heat treated so they don't wear out too fast.

The pin with a screwdriver slot is a stop for the tail stock. This keeps it from falling off if you're not paying attention.
 

Another nice feature on this tail stock is being able to tell how far you have traveled while drilling or reaming. And you can reset a zero if you need to. This can be very handy if you have a depth that you need to deal with because some lathes don't have this feature.
 

Below you can see the carriage, which includes the apron, saddle, compound rest, cross slide and tool post (which is just out of view).

The lever with the red handle is to power the spindle. Pull it up and it turns counterclockwise (when looking at it from the tail stock) but this is called forward. Pull to the right and then down and the spindle turns in reverse.

The lever above that is to engage the half-nut, which is used for threading. See the dial with the numbers 1 thru 4 on it? That housing pivots making contact with that long threaded shaft called a 'lead screw'. As the lead screw turns, so does the dial. Depending on the thread that you're cutting, you wait for a certain number to lineup with that dot at the bottom of the dial. Once it's lined up, you push on that lever to engage that half-nut and your desired thread starts cutting. This takes some practice because it's easy to miss your mark your first few times.

That shorter lever is to engage the feed for the cross slide (in or out) or longitudinal (left or right). You pull out and up for the cross slide or you push in and down for the longitudinal feed.

The two hand wheels are for moving the cross slide (small diameter) or the carriage (large diameter). They both have a dial on them that you can 'zero-out' depending on what you're working on. And if you're using these without engaging any levers, then you are doing the feeding.
 

Here is a better shot of the compound rest and tool post. The numbers on that scale are in degrees that line up with a stationary mark next to that nut. BTW, there are two of those nuts, one on either side. Once these are loose you can rotate it for different applications. As you can see it's set to zero but that can change depending on what you might be working on.