Anchor points are placed with the Pen Tool. The Pen Tool basically places a handleless anchor point wherever you click on the image window. If you click-hold-drag a handle appears (with the resulting curve in the line). You can leave the path either open or closed. To close the path click the final segment on the first anchor point of the path.
The Freeform Pen Tool places anchor points automatically as you draw on the image. You can also use the Pen Tool magnetically by checking the box on the toolbar. I don't use the Freeform Pen Tool (or the magnetic option) very often because even though it makes a good line, it often has wacky handles which makes altering the path difficult.
Lastly, the toolbar allows you to designate the path as a work path in the paths palette or as a clipping path (which appears as a layer thumbnail). The basic difference between the two is the clipping path automatically fills when you close the path, the work path doesn't fill until you tell it to. The work path has many other uses which we will cover later.
Often you will need to adjust a path after you draw it. You can add/delete anchor points with the Add/Delete Anchor Point Tools and you can convert a handless anchor point to one with handles and break handles with the Convert Point Tool. You change the anchor point directly by clicking on it and break the handles by dragging on the handle "knobs." You can move the points with the Direct Selection Tool (the white arrow located just over the Pen Tools). You can select multiple anchor points by dragging around them (or selecting them individually while holding the shift key).
You can access the Direct Select Tool and the Convert Point Tool while you are using the Pen Tool by pressing command or option resepectivelythis definitely beats going back and forth to the Tools Palette while trying to manipulate the paths and anchor points.
Use as few anchor points as possible to make your shape. This keeps your shape simple and easy to edit. In the beginning you are tempted to put more points down than you may actually need. Most curved areas can be drawn with an anchor point at the beginning and the end of the curve, you don't need one at the apex (which is quite tempting to do).
You can transform selected path points with the Transform command (Edit>Free Transform Path). Once in transform mode you can manipulate the path just as you would an image or selection (scale, rotate, etc.).