Convert the DataFrame's content (e.g. Lat and Lon columns) into appropriate Shapely geometries first and then use them together with the original DataFrame to create a GeoDataFrame.
from geopandas import GeoDataFrame
from shapely.geometry import Point
geometry = [Point(xy) for xy in zip(df.Lon, df.Lat)]
df = df.drop(['Lon', 'Lat'], axis=1)
crs = {'init': 'epsg:4326'}
gdf = GeoDataFrame(df, crs=crscrs="EPSG:4326", geometry=geometry)
Result:
Date/Time ID geometry
0 4/1/2014 0:11:00 140 POINT (-73.95489999999999 40.769)
1 4/1/2014 0:17:00 NaN POINT (-74.03449999999999 40.7267)
Since the geometries often come in the WKT format, I thought I'd include an example for that case as well:
import geopandas as gpd
import shapely.wkt
geometry = df['wktcolumn'].map(shapely.wkt.loads)
df = df.drop('wktcolumn', axis=1)
crs = {'init': 'epsg:4326'}
gdf = gpd.GeoDataFrame(df, crs=crscrs="EPSG:4326", geometry=geometry)