I agree with everyone else, unless you are a very intrepid driver and/or are already familiar with the city I would avoid driving into the city.
It looks like the nearest commuter rail station to Burlington is in Woburn, the next town over. This may or may not work out for you depending on where in Burlington you are staying.
On the MBTA web site they have a trip planner tool: http://www.mbta.com/rider_tools/trip_planner/
When I put Burlington MA as a starting point and downtown Boston as an ending point they have you taking a bus from Burlington to the Alewife T station at the northwest end of the Red Line subway line, then taking the subway into town.
That is certainly one way to do it, Alewife also is one of the stations with a huge parking lot although it fills up early in the day during the work week.
Your hotel might also be able to give you a rundown of available options…they might have a shuttle to one of the public transit stations, for instance.