how set column as date index?

Your question lacked a proper explanation, but you can do the following:

In [75]:
# convert to datetime
df['Date'] = pd.to_datetime(df['Date'])
df.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 23 entries, 0 to 22
Data columns (total 2 columns):
Date     23 non-null datetime64[ns]
Value    23 non-null float64
dtypes: datetime64[ns](1), float64(1)
memory usage: 448.0 bytes

In [76]:
# set the index
df.set_index('Date', inplace=True)
df.info()

<class 'pandas.core.frame.DataFrame'>
DatetimeIndex: 23 entries, 1988-01-01 to 1988-01-23
Data columns (total 1 columns):
Value    23 non-null float64
dtypes: float64(1)
memory usage: 368.0 bytes

So here to_datetime will convert date strings to datetime dtype, set_index with param inplace=True is all you need,