How to list groups in a view

You are close, you just need to add one more relationship. Group membership -> Group membership: Group gid. That loads the group from the group membership and makes fields on the group available.

Since you are trying to display groups though I would create a view like this. This one is displaying groups and uses a relationship to group memberships and a uid as a contextual filter to display only groups the uid is a member of.

$view = new view();
$view->name = 'test_group_memberships';
$view->description = '';
$view->tag = 'default';
$view->base_table = 'groups';
$view->human_name = 'Test group memberships';
$view->core = 7;
$view->api_version = '3.0';
$view->disabled = FALSE; /* Edit this to true to make a default view disabled initially */

/* Display: Master */
$handler = $view->new_display('default', 'Master', 'default');
$handler->display->display_options['use_more_always'] = FALSE;
$handler->display->display_options['access']['type'] = 'none';
$handler->display->display_options['cache']['type'] = 'none';
$handler->display->display_options['query']['type'] = 'views_query';
$handler->display->display_options['exposed_form']['type'] = 'basic';
$handler->display->display_options['pager']['type'] = 'none';
$handler->display->display_options['pager']['options']['offset'] = '0';
$handler->display->display_options['style_plugin'] = 'default';
$handler->display->display_options['row_plugin'] = 'fields';
/* Relationship: Group: Group membership */
$handler->display->display_options['relationships']['group_membership']['id'] = 'group_membership';
$handler->display->display_options['relationships']['group_membership']['table'] = 'groups';
$handler->display->display_options['relationships']['group_membership']['field'] = 'group_membership';
/* Field: Group: Group ID */
$handler->display->display_options['fields']['gid']['id'] = 'gid';
$handler->display->display_options['fields']['gid']['table'] = 'groups';
$handler->display->display_options['fields']['gid']['field'] = 'gid';
/* Field: Group: Title */
$handler->display->display_options['fields']['title']['id'] = 'title';
$handler->display->display_options['fields']['title']['table'] = 'groups';
$handler->display->display_options['fields']['title']['field'] = 'title';
/* Contextual filter: Group membership: User uid */
$handler->display->display_options['arguments']['user']['id'] = 'user';
$handler->display->display_options['arguments']['user']['table'] = 'group_membership';
$handler->display->display_options['arguments']['user']['field'] = 'user';
$handler->display->display_options['arguments']['user']['relationship'] = 'group_membership';
$handler->display->display_options['arguments']['user']['default_argument_type'] = 'fixed';
$handler->display->display_options['arguments']['user']['summary']['number_of_records'] = '0';
$handler->display->display_options['arguments']['user']['summary']['format'] = 'default_summary';
$handler->display->display_options['arguments']['user']['summary_options']['items_per_page'] = '25';

As ctrlADel has said above: If you want a view of groups, I suggest you create such a view and then you can easily add the groups' fields to the view. If you want a view which lists more than just groups, I suggest you try to decide which "base table" makes most sense and go from there.

For instance: If you want a list of nodes with a field saying what group they're in, start with a node view and add a "Node: Parent group" relationship to the group they belong to. If you want a list of groups with one field listing the amount of nodes in the group, start with a group view and add a relationship to "Group: node content" and work with that.

I'm using the relationship User: Group membership to get the groups a user is a member of and the field Group membership: Group gid (Group gid) but can't figure out how to get the name from the gid.

In this case, you need to create a Group view and add a relationship to the group members. Then you can add a contextual filter on the membership's uid property. Or, in case you also want to show the user's fields in the view, you could even add a 2nd relationship from the membership to the user and contextually filter on the user's uid.

Seems solved. Added to howtos.

Adding fix credit.