AutoCAD Civil 3D and ArcGIS

In CAD:

Import Shapefile to CAD:

MAPIMPORT

Export Polylines as Polygons to GIS:

MAPEXPORT

Querying Shapefile in CAD:

Change the Workspace from Civil 3D to Planning and Analysis
Home Tab -> Palettes Panel -> Map Task Pane
Manage data content -> Connect to Data
Add SHP Connection -> Browse to the Shapefile -> Connect
Add to Map -> Add to Map with Query

Insert SID files as images in CAD:

Change the Workspace from Civil 3D to Planning and Analysis
Home Tab -> Data Panel -> Insert an Image button (middle button to the right of the Attach button)
Change the file type to MrSID and select your file.
Reference

Using Geolocation:

Toolspace -> Settings -> right-click on Drawing and select Edit Drawing Settings
Set the coordinate system
Geolocation Tab -> Online Map -> Select your map style
To print high quality:
Go to your viewport and select capture area.
In model space, select your captured image and adjust the resolution to Very Fine.

In GIS:

Import CAD DWG by Converting to Geodatabase:

Go to ArcToolbox
Go to Conversion Tools
Select To Geodatabase
Reference

Save your Map as a TIFF to use as an image in CAD:

Go to File and then Export Map
Change the File Type to .TIFF and save it in the appropriate folder with the right name.
Reference 

Merge Polygons:

Bring your source polygon files into GIS.
ArcToolbox>Analysis Tools>Overlay>Union

Finding Overlapping Polygons:

ArcToolbox>Analysis Tools>Overlay>Intersect
Inspect each new overlapping polygon.
Refine your source files.
Bring the source files back into GIS.
Run the intersect tool again until there are no more overlapping polygons.

Removing Overlapping Polygons:

Merge your polygons using the Union Tool.
Using the Editor, Start Editing.
Select the polygons you want to delete, right-click and select delete.
Save your edits and stop editing.

Copying Attribute Date to Excel:

Open Attribute Table
Select the upper left-hand corner of the table while holding down CTRL.
Right-click in the far left side of the table and select "Copy Selected."
Paste data into your Excel Spreadsheet.
You can now process your data in excel (ex. subdividing areas with multiple classifications, breaking them up by type and summing up their areas)

Working with Coordinates and Coordinate Systems:

If your points are in the right coordinate system but only show lat/long:
Run "add XY coordinates" from the data management Toolbox to add Easting and Northing to the attribute data.
You can extract the attribute data, paste into excel and create a csv to import your points as COGO points in your drawing.

If your points/shapes are in the wrong coordinate system:
Run "project" to the correct system.
You can export your points/shapes to CAD and copy and paste them into your drawing. If you need them as COGO points, run "add XY coordinates" to add them to your attributes and create a csv for import into your drawing.

You can also use the Earth Point website to convert between coordinate systems if you have a subscription. Without a subscription you can still use the website, but you can only convert five sets of coordinates at a time.
Reference