I have the following dataframe:

Date        abc    xyz
01-Jun-13   100    200
03-Jun-13   -20    50
15-Aug-13   40     -5
20-Jan-14   25     15
21-Feb-14   60     80

I need to group the data by year and month. I.e., Group by Jan 2013, Feb 2013, Mar 2013, etc...

I will be using the newly grouped data to create a plot showing abc vs xyz per year/month.

I've tried various combinations of groupby and sum, but I just can't seem to get anything to work. How can I do it?

You can use either resample or Grouper (which resamples under the hood).

First make sure that the datetime column is actually of datetimes (hit it with pd.to_datetime). It's easier if it's a DatetimeIndex:

In [11]: df1
Out[11]:
            abc  xyz
Date
2013-06-01  100  200
2013-06-03  -20   50
2013-08-15   40   -5
2014-01-20   25   15
2014-02-21   60   80

In [12]: g = df1.groupby(pd.Grouper(freq="M"))  # DataFrameGroupBy (grouped by Month)

In [13]: g.sum()
Out[13]:
            abc  xyz
Date
2013-06-30   80  250
2013-07-31  NaN  NaN
2013-08-31   40   -5
2013-09-30  NaN  NaN
2013-10-31  NaN  NaN
2013-11-30  NaN  NaN
2013-12-31  NaN  NaN
2014-01-31   25   15
2014-02-28   60   80

In [14]: df1.resample("M", how='sum')  # the same
Out[14]:
            abc  xyz
Date
2013-06-30   40  125
2013-07-31  NaN  NaN
2013-08-31   40   -5
2013-09-30  NaN  NaN
2013-10-31  NaN  NaN
2013-11-30  NaN  NaN
2013-12-31  NaN  NaN
2014-01-31   25   15
2014-02-28   60   80

Note: Previously pd.Grouper(freq="M") was written as pd.TimeGrouper("M"). The latter is now deprecated since 0.21.

I had thought the following would work, but it doesn't (due to as_index not being respected? I'm not sure.). I'm including this for interest's sake.

If it's a column (it has to be a datetime64 column! as I say, hit it with to_datetime), you can use the PeriodIndex:

In [21]: df
Out[21]:
        Date  abc  xyz
0 2013-06-01  100  200
1 2013-06-03  -20   50
2 2013-08-15   40   -5
3 2014-01-20   25   15
4 2014-02-21   60   80

In [22]: pd.DatetimeIndex(df.Date).to_period("M")  # old way
Out[22]:
<class 'pandas.tseries.period.PeriodIndex'>
[2013-06, ..., 2014-02]
Length: 5, Freq: M

In [23]: per = df.Date.dt.to_period("M")  # new way to get the same

In [24]: g = df.groupby(per)

In [25]: g.sum()  # dang not quite what we want (doesn't fill in the gaps)
Out[25]:
         abc  xyz
2013-06   80  250
2013-08   40   -5
2014-01   25   15
2014-02   60   80

To get the desired result we have to reindex...