How to move data from big table
Couple of additions to Rolando's suggestion.

If you're clearing out the old table, as well as populating new you could use the OUTPUT clause. Be mindful of the potential for log growth, consider a loop/batch approach if this may be a problem.

DELETE
    OldDatabase.dbo.MyTable
OUTPUT
    DELETED.col1
    , DELETED.col2
    , DELETED.col3
INTO
    NewDatabase.dbo.MyTable


BCP is a handy alternative to be aware of. Note this is using SQLCMD syntax.

:setvar SourceServer OldServer
:setvar SourceDatabase OldDatabase
:setvar DestinationServer NewServer
:setvar DestinationDatabase NewDatabase
:setvar BCPFilePath "C:\"

!!bcp "$(SourceDatabase).dbo.MyTable" FORMAT nul -S "$(SourceServer)" -T -n -q -f "$(BCPFilePath)MyTable.fmt"
!!bcp "SELECT * FROM $(SourceDatabase).dbo.MyTable WHERE col1=x AND col2=y" queryout "$(BCPFilePath)MyTable.dat" -S "$(SourceServer)" -T -q -f "$(BCPFilePath)MyTable.fmt" -&gt; "$(BCPFilePath)MyTable.txt"
!!bcp "$(DestinationDatabase).dbo.MyTable" in $(BCPFilePath)MyTable.dat -S $(DestinationServer) -T -E -q -b 2500 -h "TABLOCK" -f $(BCPFilePath)MyTable.fmt