How do do I change the anchor point of a layer?

As Jane has said, the anchor point does not show unless enabled in Preferences Tools, and the default — as in after you reset Prefences for instance — is for it to be turned off.  However you can turn it on by checking the box I have highlighted with Green.  You can snap the point to the corners and mid points using the grid I have highlighted in red.  After this the entire object will move, and the only way to free it is to hold down the Alt (Opt) key and drag.

Another way to position the anchor point is to use the X, Y, coordinates to the right of the grid I pointed out.  This can be especially useful when using Free Transform Snap & Repeat when you need to be 100% accurate to prevent an error building up.  In this case you would reposition in the Ruler 0, 0 point, and use that as a reference for your artwork.

So in the example below I have dragged out guides to the centre of the image, and dragged the ruler 0,0 to the guide intersection

I'm going to use Step & Repeat to accurately position the numerals around a clock face.

I've created the first number at the 12 o'clock position and centered it.

Copied the number, but I need the handle to be exactly on the cetre point.  I can do that by moving it roughly into position, and then entering zero in the X and Y coordinates in the Options bar.  It is important to position the handle before entering the angle, which will be 360° / 12 = 30° 

OK that and you have the next numeral at the one o'clock position.

Now use Step & Repeat which Shift Ctrl Alt T (Shift Cmd Opt T) another eleven times to automatically create and position the rest of the numerals. Note: If you use Step & Repeat 12 times you can test the acuracy because the last numeral should exactly cover the first numeral. 

Edit the Type layers to change theire values, and rotate numbers 4 to 8 by 180° and it is job done

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@Delphi Lily wrote:

It was much easier in the old versions when the anchor point was in the middle of a picture and all you had to do was move it. But how do I move the anchor point in the new versions?

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Layers don't have anchor points, but vector shapes do. If you are working with a vector shape or a path, use the Direct Selection tool to adjust the anchor point. Deselect first, then select the anchor points you need to move. Shift selects muliples.

Jane