The Alignment Panel allows you to set the alignment of an element relative to its parent (or to the page.)  This will keep the element pinned to the left side, right side, or aligned exactly in the center of its parent, regardless of the size of the device that you are viewing it on.

To open the Alignment Panel, click the icon in the right toolbar, select it from the "Window" menu, or press Shift A on your keyboard.

Click one of the three options to set a selected element to left-, right-, or center-aligned.
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Depending on what type of element you currently have selected on the stage, you may also see alignment controls appear in the contextual toolbar at the top of the screen.
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Note that this is not the same thing as text alignment. The Alignment Panel can be used to adjust the alignment of the element overall, but not the content within it. To set the alignment of text within an element, you'll need to use the Text Formatting Panel.
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If you have two elements that you want to arrange in a side-by-side layout, use the Alignment Panel to give one element a left-alignment, and then other a right-alignment, or make them both left- or right-aligned. Then adjust the width of each element, so that the total is 100% or less (for example, give each element 50% width, or give one 25% width and the other 75%, etc.)