How can I determine if a user is logged in, and who that user is? I'm running some checks to see if there is a user logged in, and if that user is someone specific. When accessing user.isCurrent it's returning 1 when I'm logged in, but returns null when I'm not. Should this be returning 0 or false in that case, or should I be checking {% if user.isCurrent is defined %} ?
To determine if the user is logged in at all, you'll want to use the currentUser variable:

{% if currentUser %}
    Welcome, {{ currentUser.friendlyName }}!
{% endif %}


To determine if the logged in user is a specific user, then simply compare against their username:

{% if currentUser and currentUser.username is 'johndoe' %}
    Hey Johnny Boy!
{% endif %}


The isCurrent method is useful when targeting a more generic UserModel (where you don't know if the user would be the current user).

{% for user in craft.users %}
    {% if user.isCurrent %}
        {{ user.friendlyName }} is you!
    {% else %}
        {{ user.friendlyName }} is someone else.
    {% endif %}
{% endfor %}