Consider this scenario, my database table has 300000 rows and has a fulltext index. Whenever a search is done it locks the database and doesn't allow anyone else to login to the portal.
Any advice on how to get things sorted out here will be really appreciable.
Does logging on perform a write to the table? eg. a 'last visit' time?
If so you may expect behaviour something like this because MyISAM writes do a lock over the entire table. Usually this is avoided by not using noddy MyISAM and going to InnoDB instead, which has row-level locking (amongst other desirable database features).
The problem, of course, is that you only get fulltext search with MyISAM.
So you'll need to split your tables up. If you can keep the read-heavy and fulltext stuff in a different table to the stuff that needs writing (but linked using the same primary key), you can probably make it so that the two operations don't affect each other.
Better, migrate the bulk of the table to InnoDB, leaving only a fulltext field in MyISAM. Everything except fulltext searches can then steer clear of the MyISAM table, and use only the InnoDB table which exhibits much better locking performance. Personally, I now tend to store everything in the InnoDB table, including the text, and store a second copy of the text in the MyISAM table purely for fulltext searchbait purposes; this simplifies queries and code and brings the advantages of InnoDB's consistency to the text content, and I also use it to process the searchbait to get stemming and other features MySQL's fulltext doesn't normally support. But it does mean you have to spend a lot more space on storage.
You can also improve matters by cutting down number of writes. For example if it is a 'last visit' timestamp you're writing, you can avoid writing that unless, say, a minute has passed between the previous time and now, on the basis that no-one needs to know the exact second someone last accessed the site.
If you use an external search engine or MySQL search plug-ins Lucene or Sphinx, they should be able to read and index without locking the table. They store a local version of the indexed records, so they don't have to read the table very often, and never need to write to it.