Create design and then goto edit menu and Photoshop define pattern command and give it a name and OK. The area will be the entire image, you can get around this by using selections to cover the area you wish to use.
Another option is to use a selection. Select an area using the marquee tool in toolbar and Edit menu and Define command and give the tile a name and then click OK. The result will probably not be seamless though unless the image or the selection is seamless to start with.
A great way to make seamless design is to use the view menu and new guide layout (such as 4 x 4) and then use the cells of the guides to make a seamless design. The selection can then use the same guides to create the tile.
You can create all kinds of seamless designs by using offset filter. You can use resources such as brush strokes, you can use images, you can apply pixel shapes, you can reduced sized images, you can combine with other resources etc but the key thing is to avoid the seams so any brush stroke or shape added should avoid the edge. If you use a layer, you will need to flatten the layers. The possible designs are infinite such as diamond designs, binary code / computer code designs, polka dot designs and many more.
Start with an empty document say 1000 x 1000. Go to the custom shape tool or brush tool or image and add that to the middle of the image / document. Filter menu and other and offset command and set to -500 and 500 and wrap (go for half of the size). Add additional designs in the middle of the current document avoiding the edges. Add the preset via the method described above.
Open an imageand select part of the image and copy Goto the file new command and set the new document to height x 2 and width x 2 and then edit menu and paste. Probably easier to have to smart guides on show smart guides (View menu show command) or you can use guides via the view menu and new guide layout with a setting of 2 and 2.
Position that copied image layer in the top left of the new document for the first part of the creation and then alt / option duplicate layer and shift to the top right and bottom left and bottom right and then select bottom items and edit menu and flip vertical and select the two layers on the right and edit menu and transform and flip horizontal and flatten image via the layer menu. Add the preset using the methods described above. You can, of course, use a set of guides for 3 x 3 10 x 10 etc to create more complex tiles
The pattern preview makes it super easy to create all kinds of designs and then create them via the edit menu. You can use this approach to create many different designs using stripe line designs, triangular artwork tiles, circular designs, etc Super useful feature for creating artwork with brushes and shapes etc as it will duplicate the design for you. Sadly, there is no button to be able to click to save your tile quickly
You can use the same design but with an adjustment added which means a red design can be saved and then a blue design can be saved and then green etc You can add an adjustment layer on top of all the layers and then modify the properties of the adjustment via the properties panel. The adjustment layer can be added via the layer menu and new adjustment layer command.
You can create seamless tiles using a gradient by setting the stops. The easiest ones to use can be the linear as well as the reflected but all the types can be used such as using the gradients with selections and then create via the edit menu and that is stored to the presets panel. You can combine gradients using blending modes of difference etc
You can find this via the window menu. This is a new feature and it is a super way to add the artwork to the image as you just need to drag the preset from the panel to the art board.
You can now also quickly search for a particular tile as long as it has been named, you can find it via the panel and the top 'search' so when you are creating your tiles, make certain that you give it a sensible name as that will make finding it again super easy