I am fairly new at using Adobe Illustrator. I am trying to recreate this pattern in the circle but have no luck in finding answers to make it. I've already created the circle and the star except for that pattern. If anyone could help in explaining how to create the pattern circled in the picture AND explain how to change the color of the pattern, that would be great! Thank you.
The pattern doesn't look especially regular, so it can well be drawn with the Pen as already said by others. The small size makes exact observations impossible. I guess you have a higher resolution version. With it you can simply make manual tracing which means manually drawing over with the pen the same shapes keeping the original as the reference. Remember to lock the original.
If you are a beginner you surely need hours of practicing before the Pen starts to produce the wanted Bezier curves with acceptable accuracy. In addition you must learn how to edit nodes and handles with the direct selection tool + remove & add nodes (=anchors in Illustrator's menus and manuals)
If you can accept something resembling which is more regular (=simpler) you can do it without the pen. But still a good amount of Illustrator knowledge is a must.
Draw a square (=rectangle holding Shift)
Apply Object > Transform Rotate > 45 degrees.
Apply Object > Path > Add Anchor points to get midpoint anchors. A rectangle originally has only 4.
In this phase at last is useful to select all and apply Object > Transform > Reset bounding box to straighten the bounding box which is rotated after step 2.
The Direct selection tool (=white arrow) can be used to select anchors and move them.
Make a copy (=drag holding Alt-key) and make a stretched version:
The 3 rightmost anchors are selected and moved to right with the direct selection tool. Holding Shift key forces the movement horizontal (or vertical or 45 degrees depending on which is nearest). The green line is a smart guide which pops visible automatically to show horizontal and vertical sameness.
It's a good idea to keep View > Smart guides and Snap to point ON for exact placements. Other snaps are generally harmful if they are not needed, so let them be OFF
The next cartoon shows more steps:
The original square and the stretched copy.
Make a flipped copy of the stretched shape. Apply Object > Transform > Reflect > Vertical > Copy. The red square is drawn to be used as temporary measurement stick. The blue copies of it show how it's used to place the items. NOTE: If you deselect all, then select a shape and drag its one anchor with the direct selection tool the others follow and the dragged anchor snaps exactly if you have snap to point ON.
Draw a line (=red) on the edge of the shape drag it longer under the mid square. Hold the shift key when you drag with the black arrow a corner. You keep the proportions and directions by holding the shift key when you make something bigger or smaller. Drag the mid square bigger so that the corner hits the red line. Hold Alt+Shift to keep the midpoint intact.
Select all and apply Object > Envelope Distortion > Make with Warp > Arc to get a curved version. The percentage is "how many percents the arc should be of 180 degrees"
Everyone do not love calculations. Fortunately there's other ways to bend shapes. One is to use the shape as a brush:
If you drag a shape to the Brushes collection you can define the shape to be an Art Brush or Pattern Brush or Scatter Brush. I selected "Pattern Brush" and "Add space to fit". In the image you see 2 black curves and the result when I applied my new pattern Brush to them. The shape was colored to blue before dragging it to the Brushes.
Learn from user's Guide the details of the brush versions.