The Photoshop count tool can be found in the toolbar. The exact location may vary as you can be re-position via the customization and it may also be found in the extras sections. It doesn't come with any options that can be displayed when you double click the icon.
However, the options are available along the control bar and you can set a group as well as rename it as well as set the visibility of said group as well as the color as well as the size of the marker and label.
It can be used by simply clicking the current image in different locations. It is a great way to add references to an image. Select the tool. Click the art board to add a marker / label at a particular position. The item will be part of a group and will have the current set color as well as the current marker size and label size. This is useful for observations, medical purposes etc
All the marker information is stored with the document if you save the file as a PSD document so when you re-open the PSD you will still see them (or not depending on the visibility)
Select it and click in the document and you will see a 1 added. Click somewhere else with it and you will see a number two and then click again to generate a number three and so on. Hold down the alt / option key down and hover over the 1 You will see 1- etc and click and then the number one is deleted.
OK, once you have your markers on your art board, what else can you do with them ? Well, you can delete it by holding down the alt / option and a little minus sign will appear when you hover over the entry and you can then click it to remove it. You can also clear them all in a second by clicking the clear button. Once you delete or clear them, all the others will shuffle down one.
You can move them, they are not cast in stone. With the it selected, hover over the indicator and select and move the item. Have to say, it is not the easiest operation as you have to avoid getting the plus to appear and then move the marker / label.
You can can also hold down the shift key to hold it in vertical and horizontal. Personally, I wish there were a little more such as perhaps a grid feature or alignment and distribution features.
You could, of course, simply display a set of guide lines via the view menu and new guide layout and add the markers and labels to the intersections of the lines of the guides
You can keep them blue but you can change the color via the color field for the current set. You can change it to green or red and all the current items in the same group will be changed as well.
The initial entries are added to a first set. If you change the color / size etc then all are changed for that set. The sequence starts as 1, 2, 3, 4, 5 etc. If you go to the folder in the control bar (next to the bin) and you can add a new set. If you have that selected, the markers will then be 1, 2, 3, etc for that and it can have its own size / color / label. You can have multiple sets of these markers.
The details of the generated markers and labels can be recorded to the measurement log (found in the window menu). Add the markers etc and then click the record measurements and an entry will be added to the log. Sadly, it does not record the location of the marker but it does record the existence of them.
They are not really there, they are purely a visual display and they are not part of the document. There is little beyond capturing a screenshot of all the markers and then flattening that. Of course, you can always just use the horizontal type and add them on top of the markers, which is not really ideal. This does show that though this feature is useful, you could do much the same with just creating a layer that includes all the markers made by the horizontal type.