How can I know when SQL Full Text Index Population is finished?

I would like to offer an easier-to-read version of @Daniel Renshaw's answer:

DECLARE @CatalogName VARCHAR(MAX)
SET     @CatalogName = 'FTS_Demo_Catalog'

SELECT
    DATEADD(ss, FULLTEXTCATALOGPROPERTY(@CatalogName,'PopulateCompletionAge'), '1/1/1990') AS LastPopulated
    ,(SELECT CASE FULLTEXTCATALOGPROPERTY(@CatalogName,'PopulateStatus')
        WHEN 0 THEN 'Idle'
        WHEN 1 THEN 'Full Population In Progress'
        WHEN 2 THEN 'Paused'
        WHEN 3 THEN 'Throttled'
        WHEN 4 THEN 'Recovering'
        WHEN 5 THEN 'Shutdown'
        WHEN 6 THEN 'Incremental Population In Progress'
        WHEN 7 THEN 'Building Index'
        WHEN 8 THEN 'Disk Full.  Paused'
        WHEN 9 THEN 'Change Tracking' END) AS PopulateStatus

Results:

LastPopulated           PopulateStatus
----------------------- ----------------------------------
2012-05-08 14:51:37.000 Idle

(1 row(s) affected)

You can query the status using FULLTEXTCATALOGPROPERTY (see here: http://technet.microsoft.com/en-us/library/ms190370.aspx).

For example:

SELECT
    FULLTEXTCATALOGPROPERTY(cat.name,'ItemCount') AS [ItemCount],
    FULLTEXTCATALOGPROPERTY(cat.name,'MergeStatus') AS [MergeStatus],
    FULLTEXTCATALOGPROPERTY(cat.name,'PopulateCompletionAge') AS [PopulateCompletionAge],
    FULLTEXTCATALOGPROPERTY(cat.name,'PopulateStatus') AS [PopulateStatus],
    FULLTEXTCATALOGPROPERTY(cat.name,'ImportStatus') AS [ImportStatus]
FROM sys.fulltext_catalogs AS cat

You might also like to use SQL Profiler to monitor what commands SQL Server Management Studio issues when you bring up the properties dialog for the catalog. The dialog includes an indicatin of population status and all the information shown is queried using T-SQL.