Please help identify the type of weed and what treatment is recommended.
The weed looks like veronica or speedwell. The flower of this weed is blue http://extension.umd.edu/hgic/speedwell
In flower beds you will have to handpull. In the lawn you can use a postemergent herbicide. See the attached publication for more information http://www.mdturfcouncil.org/admin/uploadfiles/tt-49-broadleaf-weed-control.pdf