To create a seamless pattern is, at first glance, a complex operation. However, it is remarkably simple in reality and with a bit of practice.
To effectively replicate this technique, it is highly recommended that you have a graphics tablet of some kind. It doesn't need to be fancy, just that it uses a stylus. Trust me, doing this with a mouse will destroy your wrist in no time at all.

Now, there are several techniques to creating a seamless texture. On you may or may not have heard of is by mirroring the texture and using the Clone Stamp to remove the seam. While this works, it ends up looking bad, particularly if you are only using a small pattern, or if the pattern has little variety and in the end can be rather tedious and irritating with a poor result to show for it. However, there is an interesting tool available in Photoshop called Offset (Filters-Other-Offset) that is much more effective. It moves, or offsets , the image so many pixels along the X (left-right) and Y (Up-Down) axis, whilst moving the part of the image that went off screen to the area that is left empty, similar to how the Pattern layer works.

Do this with your image, make it offset about 1/3 of the image width and height. After doing this, duplicate this layer as a backup.

Now, there is an obvious seam visible which must be removed. This is done by using the Clone Stamp tool. Selecting this tool, hold Alt and click on an area of your pattern you want to clone somewhere. Try and think ahead as to which direction you are painting and select a source accordingly.

As I'm sure you can see in this image, the circle is your brush cursor. The cross is your clone source, which will move according to your brush starting from where you sourced from. When painting, use a solid brush at full opacity and flow. A smaller brush is useful for drawing outlines for patterns whilst a larger one is best left for filling in the colour. Try and keep the colour as uniform as possible and use the Clone Stamp to remove any variations or blemishes.

Continue doing this, all the while trying to keep your pattern the same or as similar as you can get to the original. Take your time with this process, the more effort and time you put in, the better the result.

When you are finished, duplicate the layer again to back it up, then run the Offset filter again. This is to check for any seams you may have created during the previous step. Correct these and repeat the process until there are no more seams.
After this is finished, create a pattern out of your image by going to "Edit-Define Pattern" and test it out by creating a pattern layer and setting the scale to 50%. Hopefully, it should be nice and seamless.