Surface-Mount Prototyping (AXL 335 & SFH 7050)
Your first go at it should be to try to find these or suitable replacements in an already-mounted format, either in dev boards, or from a prototyping supplier like SparkFun.

Second, you can try to make your own circuit boards. These packages are challenging because it is very, very difficult to just use an iron.

There are two ways you can go on this IMO:

1) Reflow paste. Because these are no-lead packages, you'll need to control the paste thickness carefully, which pretty much means a solder stencil. Once you have the paste down, put your part on, preheat the board to a particular temperature and apply hot air. You can also use the hot-plate method that @Robherc mentions.

2) Try a soldering iron anyway. I noticed that the ADXL doesn't require you to solder down the center pad, so you might be able to get away with extending the footprint pads out a little beyond the recommended pad size, just enough to get an iron and a dob of solder on. This hopefully will wick up into the pad and make contact with the component lead.

3) Give it to a professional rework shop. It's expensive, but you might be able to get the 'student discount' if you are pleasant enough.

Obviously all of these require you to design a custom circuit board, which you may not be able to get away from...