Magento Shipping – Get Shipping Methods via Observer

There are many ways to do this but i am sharing with you the best method i know of. - See more at:

Detail LINK

let me know if i can help you more

EDIT

Here i am giving you sudo code

 if ($this->_checkChangedAddress($bill_data, 'Billing', $bill_addr_id) || $this->getRequest()->getPost('payment-method', false))
        {
            if (isset($bill_data['email']))
            {
                $bill_data['email'] = trim($bill_data['email']);
            }

        $bill_result = $this->getOnepagecheckout()->saveBilling($bill_data, $bill_addr_id, false);

        if (!isset($bill_result['error']))
        {
            $pmnt_data = $this->getRequest()->getPost('payment', array());
            $this->getOnepagecheckout()->usePayment(isset($pmnt_data['method']) ? $pmnt_data['method'] : null);

            $result['update_section']['payment-method'] = $this->_getPaymentMethodsHtml();

            if (isset($bill_data['use_for_shipping']) && $bill_data['use_for_shipping'] == 1 && !$this->getOnepagecheckout()->getQuote()->isVirtual())
            {
                $result['update_section']['shipping-method'] = $this->_getShippingMethodsHtml();
                $result['duplicateBillingInfo'] = 'true';

                $ship_updated = true;
            }
        }
        else
        {
            $result['error_messages'] = $bill_result['message'];
        }
    }

Magento shipping method is depends on shipping address . first load quote shipping address then get shipping method from shipping address and code should like this

 $quoteShippingAddress = $quote->getShippingAddress();
        if(!is_null($quoteShippingAddress->getId()) ) {

 $quoteShippingAddress->collectShippingRates()->save();
     $groupedRates = $quoteShippingAddress->getGroupedAllShippingRates();
            $ratesResult = array();
            foreach ($groupedRates as $carrierCode => $rates ) {
                $carrierName = $carrierCode;
                if (!is_null(Mage::getStoreConfig('carriers/'.$carrierCode.'/title'))) {
                    $carrierName = Mage::getStoreConfig('carriers/'.$carrierCode.'/title');
                }

                foreach ($rates as $rate) {
                    $rateItem = $this->_getAttributes($rate, "quote_shipping_rate");
                    $rateItem['carrierName'] = $carrierName;
                    $ratesResult[] = $rateItem;
                    unset($rateItem);
                }
            }

}

$result is give shipping method list

2.As amasty say,shipping method are enabled from admin.Also you can do this by programmatically:

 $groups=array();
shippimgmethodcode='freeshipping';
$groups[$shippimgmethodcode][fields][active][value]=true;
Mage::getModel('adminhtml/config_data')
    ->setSection('carriers')
    ->setWebsite(null)
    ->setStore($StoreId)
    ->setGroups($groups)
    ->save();