I need to know how to create a crosstab query

This type of transformation is called a pivot. You did not specify what database you are using so I will provide a answers for SQL Server and MySQL.

---

SQL Server: If you are using SQL Server 2005+ you can implement the PIVOT function.

If you have a known number of values that you want to convert to columns then you can hard-code the query.

select typename, total, Deployed, Inventory, shipped
from
(
  select count(*) over(partition by t.typename) total,
    s.statusname,
    t.typename
  from assets a
  inner join assettypes t
    on a.assettype = t.id
  inner join assetstatus s
    on a.assetstatus = s.id
) d
pivot
(
  count(statusname)
  for statusname in (Deployed, Inventory, shipped)
) piv;

See SQL Fiddle with Demo.

But if you have an unknown number of status values, then you will need to use dynamic sql to generate the list of columns at run-time.

DECLARE @cols AS NVARCHAR(MAX),
    @query  AS NVARCHAR(MAX)

select @cols = STUFF((SELECT distinct ',' + QUOTENAME(statusname) 
                    from assetstatus
            FOR XML PATH(''), TYPE
            ).value('.', 'NVARCHAR(MAX)') 
        ,1,1,'')

set @query = 'SELECT typename, total,' + @cols + ' from 
             (
                select count(*) over(partition by t.typename) total,
                  s.statusname,
                  t.typename
                from assets a
                inner join assettypes t
                  on a.assettype = t.id
                inner join assetstatus s
                  on a.assetstatus = s.id
            ) x
            pivot 
            (
                count(statusname)
                for statusname in (' + @cols + ')
            ) p '

execute(@query)

See SQL Fiddle with Demo

This can also be written using an aggregate function with a case expression:

select typename,
  total,
  sum(case when statusname="Deployed" then 1 else 0 end) Deployed,
  sum(case when statusname="Inventory" then 1 else 0 end) Inventory,
  sum(case when statusname="Shipped" then 1 else 0 end) Shipped
from
(
  select count(*) over(partition by t.typename) total,
    s.statusname,
    t.typename
  from assets a
  inner join assettypes t
    on a.assettype = t.id
  inner join assetstatus s
    on a.assetstatus = s.id
) d
group by typename, total

See SQL Fiddle with Demo

---

MySQL: This database does not have a pivot function so you will have to use the aggregate function and a CASE expression. It also does not have windowing functions, so you will have to alter the query slightly to the following:

select typename,
  total,
  sum(case when statusname="Deployed" then 1 else 0 end) Deployed,
  sum(case when statusname="Inventory" then 1 else 0 end) Inventory,
  sum(case when statusname="Shipped" then 1 else 0 end) Shipped
from
(
  select t.typename,
    (select count(*) 
     from assets a1 
     where a1.assettype = t.id 
     group by a1.assettype) total,
    s.statusname
  from assets a
  inner join assettypes t
    on a.assettype = t.id
  inner join assetstatus s
    on a.assetstatus = s.id
) d
group by typename, total;

See SQL Fiddle with Demo

Then if you need a dynamic solution in MySQL, you will have to use a prepared statement to generate the sql string to execute:

SET @sql = NULL;
SELECT
  GROUP_CONCAT(DISTINCT
    CONCAT(
      'sum(CASE WHEN statusname=""',
      statusname,
      ''' THEN 1 else 0 END) AS `',
      statusname, '`'
    )
  ) INTO @sql
FROM assetstatus;

SET @sql 
  = CONCAT('SELECT typename,
              total, ', @sql, ' 
            from
            (
              select t.typename,
                (select count(*) 
                 from assets a1 
                 where a1.assettype = t.id 
                 group by a1.assettype) total,
                s.statusname
              from assets a
              inner join assettypes t
                on a.assettype = t.id
              inner join assetstatus s
                on a.assetstatus = s.id
            ) d
            group by typename, total');

PREPARE stmt FROM @sql;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;

See SQL Fiddle with Demo.

The result is the same for all queries in both databases:

| TYPENAME | TOTAL | DEPLOYED | INVENTORY | SHIPPED |
-----------------------------------------------------
|  Desktop |     2 |        1 |         1 |       0 |
|   Laptop |     1 |        0 |         0 |       1 |
|   Server |     1 |        1 |         0 |       0 |