There are several ways to make lines and polygons from point data: digitizing or automatically generating poylgons using an extension like Hawth's Tools.
Hawth's Analysis Tools for ArcGIS is a toolbar extention to ArcMap that offers a wide array of tools, including functions that convert points to lines or polygons. The website offers lots of support and documentation, making this one of the best all-purpose utilities available--and it's free! http://www.spatialecology.com/htools/index.php
To create a new shapefile and digitize new features:
1. Open ArcCatalog.
2. Navigate to the folder in which you want to create the new line or polygon shapefile.
3. In the selected folder, choose the Contents tab. Right click inside the folder and choose New>Shapefile. Give your new shapefile a name, choose the appropriate feature type, and click Edit to choose a coordinate system. Click OK.
4. Open ArcMap and add your basemap and GPS points. Add your new EMPTY shapefile to your map.
5. Be sure you have your Editor toolbar. If you don't see it, right click in the toolbar area and choose Editor. The toolbar will appear. If desired, move the toolbar to a convenient location.
6. To begin making new features, choose Editor>Start Editing. In the Start Editing menu, be sure to choose the appropriate folder, then click Start Editing.Click Editor again and choose snapping. Be sure that you are set to snap to Vertex of the XY data layer. Turning on snapping will ensure that the corners of new lines and polygons will fall exactly on the XY point locations. If you want the lines or polygons in your new layer to connect, turn snapping for the new shapefile, as well.
7. Choose Editor>Options and under the General tab, set your snapping tolerance to 25 pixels. This will ensure that when your arrow is within 25 pixels of an XY vertex, the arrow will jump to that vertex. When you click, a new vertex will be added to your shapefile in that location.
8. Make sure your new shapefile is showing in the Target window, choose the Sketch Tool, and make sure your Task is set to Create New Feature.
9. Now you are ready to begin creating new features. Click once in each location--in order--where a new vertex is desired. You will see the line or polygon take shape as you click. Double click the last vertex to complete the feature. Choose Editor>Save Edits. Repeat as needed to add more features to your new shapefile.
10. You may edit the attribute table of the new shapefile by adding fields and entering data (see ArcMap Help for more information on editing tables).
11. When you are finished editing your shapefile, choose Editor> Stop Editing.