How to add translations for new words in Magento?

For this:

<?php echo Mage::helper('catalog')->__('Text here');?>

Add like:

app/locale/{lang_ISO}/Mage_Catalog.csv

"Text here","Translation here"

For this:

<?php echo $this->__('Text here'); ?>

Or this (in theme local.xml, note the translate attribute; also see https://stackoverflow.com/a/8408058/794071):

<reference name="top.links">
    <action method="addLink" translate="label title">
        <label>Text here</label>
        <title>Text here</title>
    </action>
</reference>

Add like:

app/design/frontend/{interface}/{theme}/locale/{lang_ISO}/translate.csv

"Text here","Translation here"

E.g.: in your theme folder:

/locale/fr_FR/translate.csv

"Inspiration","Your France Translation"

You don't really translate words. You need to translate static blocks, pages, attributes, e-mail templates and configuration related elements from the backend. To translate system strings, there's app/design/frontend/{package}/{theme]/locale/{locale}/translate.csv

{locale} could be for example de_DE for the German language used in Germany.

Modification of translation files at app/locale/{locale}/ is NOT advised as they are part of language packages and should be regarded as core elements that may get overwritten as soon as the package is updated.