On the "Format Picture Toolbar," select the "Layout" tab (the same place where you click the "Behind Text,"). Click the "Advanced" button and click to put a check in the "Lock Anchor" box. This will keep the picture from moving around with the text - unless you move the Paragraph that the picture is anchored to. If the anchor isn't locked, sometimes the picture will try to move it's attachment (anchor) and "attach itself" to a different paragraph when you add or delete text nearby.
You can also select whether the position is relative to the paragraph where it's inserted or relative to the page, but it's usually sufficient to lock it to a specific paragraph - if you can keep track of which paragraph that is.
The "Advanced" button area is the same place where you'll need to set the vertical alignment. If you want something other than Left/Right/Center for horizontal position, you can also put in dimensions for that too. The dimensional location can be confusing, and the picture may seem to move if you resize it. The dimensions are always to the top left corner of the image.
It helps when you're doing position layouts to be sure that you're in "Print Layout" viewing mode, and I find it helpful to turn on the "View All" option (in Tools|Options|View Tab, Formatting Marks section, since then you can see all the paragraph marks and the picture anchors to keep track of where they are.
Some people find the "View All" mode distracting; but once you've used it a bit I think you'll find it helpful.