To determine if a figure has reflectional symmetry, you can use a ruler, a mirror or a Mira. The idea is that if you place a line on your pattern and you see exactly the same thing on both sides of the line, then your pattern has reflectional symmetry. To make sure your line is actually a mirror line or a line of reflection, you can fold the pattern along the line and hold your paper up to the light. If all the lines determining the drawing coincide with each other, then you have found a line of reflection.
To determine if a figure has rotational symmetry, pick a point on your picture - remember that a rotation occurs around a point. Take another piece of paper and copy a simple piece of your original pattern onto the paper. Place the copy on your original pattern and put a pencil at the point you think is the center of the rotation. If you can turn the copy around the point without moving the original pattern until your copy lines up with the original again, you have found a center of rotation. If you have turned the paper all the way around to the place where you started and haven't found a place where it lies exactly on top of the originial, then your figure does not have rotational symmetry.
To determine if a figure has translational symmetry, again make a copy of a simple piece of your original pattern. Lay this copy on top of your original and make sure that all your points lie exactly on top of one another. If you can slide your copy along the pattern in any direction until your points lie exactly on top of one another again, you have determined translational symmetry. Most repeating patterns have translational symmetry.
Glide reflection is perhaps the trickiest transformation to identify. The trick with a glide reflection is that when you slide your paper (like you did above) to find out if your pattern has translation symmetry, you must then look to see if your pattern can be reflected over a line that is parallel to the translation.
Remember that some patterns have more than one type of symmetry. Be consistent about how you check for the various types of symmetry and be sure to check for all of them in every picture.