In Magento, Customer model has an option addAttributeToFilter which helps to filter customers by attributes. For example, If We would like to get customers collections with group_id(Customer group) 3, we can use as following

$customers  = Mage::getModel('customer/customer')
    ->getCollection()
    ->addAttributeToSelect('*')
    ->addAttributeToFilter('group_id', array('eq' => 123123))
    ->load();

for user defined attribute is also same. Here customer_number is user-defined attribute:

$customers  = Mage::getModel('customer/customer')
    ->getCollection()
    ->addAttributeToSelect('*')
    ->addAttributeToFilter('customer_number', array('eq' => 123123))
    ->load();

Multiple attributes also can used with “AND” Condition

$customers  = Mage::getModel('customer/customer')
    ->getCollection()
    ->addAttributeToSelect('*')
    ->addAttributeToFilter('customer_number', array('eq' => 123123))
    ->addAttributeToFilter('group_id', array('eq' => 3))
    ->load();

Following work for OR condtion for two attributes:

$customers  = Mage::getModel('customer/customer')
    ->getCollection()
    ->addAttributeToSelect('*')
    ->addAttributeToFilter(
   array(
     array('customer_number', array('eq' => 123123))
     array('group_id', array('eq' => 3))
    )
    ->load();

For individual afterwards:

foreach ($customers as $customer)
{
   var_dump($customer->getData());
}

If the attribute is unique value then We can directly get Row:

$customer  = Mage::getModel('customer/customer')
    ->getCollection()
    ->addAttributeToSelect('*')
    ->addAttributeToFilter('customer_number', array('eq' => 123123))
    ->addAttributeToFilter('group_id', array('eq' => 3))
    ->load()
    ->getFirstItem();

Finally, If we need only selected attributes like firstname, lastname and email:

$customers  = Mage::getModel('customer/customer')
   ->getCollection()
   ->addAttributeToSelect('firstname')
   ->addAttributeToSelect('lastname')
   ->addAttributeToSelect('email');
   ->addAttributeToFilter('group_id', array('eq' => 3))
   ->load();