Select the Photoshop brush tool in the tools bar. Select the preset, size etc and symmetry options for painting along the far end of the control bar (along the top normally). Click that and you will see a menu appear and you will have options such as vertical, horizontal, dual axis, diagonal, wavy etc. Select one of those and you will see a path appear. Press return to accept it or move or re-size and rotate it.
Some of the the designs included in the list are not particularly symmetrical such as the spiral and I must admit, I find it a little fiddly to use or to get great results from. You will see a path appear but the color of the path and size depends on the settings you have given it earlier (pen tool etc)
The best options are the radial etc at the bottom of the list. You can then set the segment count though it is limited to a fairly low value of 10. Press return and then move the path and then press return again (a little odd). Once you have the path, now apply your stroke and if you have the mandala and 10 then you will have 10 lines / strokes coming from the center.
You can use the direct selection tool to modify the points of the symmetry path but for some of the paths it has no effect but if you use the curvature tool to modify the circle path, that will modify the path of the stroke. You can use the path selection tool to select the paths and move the path to a different location. You can use the path selection tool and hold down the alt / option key to duplicate the path (though it doesn't create a new path) and you can create a complex design from your stroke.
The strokes can be applied to the current layer with the path options but you can also create new layers (via the layer menu and create new layer) and create multiple layers with designs and you can use them to build up a very complex artwork.
The menu also allows you to be able to turn the effect off for the stroke (first item). You can also use the transform command to modify the path. You can also hide the path for the tool but I must admit, why, as it really does make it even more hit and miss to using the tool. Personally, stick with transformation, scale and rotate.
You can also remove the path by going to the path panel (window menu)
If you just want to create a basic mirror effect then the vertical and horizontal ones are the best to use. If you want a wonderful tile creation then select the dual axis.
You can also create your own path such as using the curvature tool and then use that a symmetry path and use it with your currently selected preset. Have to say that I have never found it particularly easy to create paths that are that useful beyond the ones that are currently available such as the dual etc
If you want to create seamless patterns with your strokes, you can use the paint tool with the symmetry and dual. Dual axis is created dead center of the document. There is no pattern preview with the feature but luckily the dual feature wraps around the document so you can draw beyond the edge and it will appear on the other side of the document so the dual is a great way to create seamless tiles with any selected strokes. You can then go to the edit menu and define command.