How to restore a database using mdf and ldf files in SQL Server 2008?
Is this possible to restore a particular database using corresponding mdf and ldf files?
  


Yes, you can try to attach them, probably just try to attach using:

CREATE DATABASE restored_copy_of_db_name
ON (filename = 'c:\temp\backup_of_mdf.mdf'),
   (filename = 'c:\temp\backup_of_ldf.ldf')
FOR_ATTACH;


It is very common for this to fail, because the log file gets damaged from this type of event (see this post for reasons we don't rely on mdf/ldf files as backups), so then you can try:

CREATE DATABASE restored_copy_of_db_name
ON (filename = 'c:\temp\backup_of_mdf.mdf')
FOR_ATTACH_REBUILD_LOG;



  
  Do we need to have any mdfs from the system databases?
  


If you're trying to restore full functionality out of the gate, then your attached database above will not include server-level logins, jobs, etc. So you may need master and msdb in order to recover some of that information (but I would attach it as a user database (msdb_copy), rather than replacing msdb, and try to restore master on a throwaway instance - see this thread for possible ideas here, but I would not be confident you'll get that info back).


  
  Steps and/or or best practices to restore that database into a new machine. 
  


Nothing really in addition to the above, except, once you have these databases back, please set up a proper backup and recovery plan, which should include periodically testing that you can restore your databases - the fact that a backup was successful is not enough to ensure you won't be doing this again.