There are several ways to accomplish what you want. You've left out some specifics such as what extensions you have available and what license level you're using, as well as how thoroughly you want to sample the raster (ie how fine is your grid). I'll make some assumptions.
The simplest, if you want a point for every cell in the DEM, is the Raster to Point tool. A point will be created at the center of every cell with an attribute that is the value of that cell. There's also the Raster to ASCII or Raster to Float tools if those would produce formats more readily imported into ACAD than a shapefile (ACAD links in the last paragraph would indicate they would work just as well as the original DEM).
If you don't want every cell, you first need to use Create Fishnet to generate the grid. There's an option called Create Label Points, which will create a separate point feature class with points at the center of every grid cell. It's simplest to use these rather than all the extra steps needed to convert your grid lines to points at the intersections (which can be done, and is discussed in other questions). Since the points are at the center of the cells, you'll need to shift your grid origin -x and -y one half of the cell x/y value to get the points where the intersections would be. For example, 10m square grid, origin at -5,-5 will put the label point at 0,0. The grid can be any dimensions you like, including identical to the DEM cell size though that would just duplicate the first method. Once you have the points, you can use the Extract Values to Points tool from Spatial Analyst as you mention to get the elevation values. You could also use the Sample tool to generate a table (not shapefile) with x and y coordinate columns as well as an elevation column.
You can also convert the raster directly to a TIN using Raster to TIN if you have 3D Analyst, however I don't know how compatible Arc's TIN format is with ACAD (if at all). That said, as Aaron mentions you should be able to add a raster DEM directly to ACAD. I found this ACAD KB article that suggests you can. There's also this blog post and a helpfile / user's guide page that covers it. In fact a quick Google search turned up a lot of results on the subject.