Make sure you have a good reason for the check. It will only be accepted to counter vandalism or disruption to Wikimedia wikis. Valid reasons include needing a block of the underlying IP or IP range, disruptive sockpuppetry, vote-stacking, and similar disruption where the technical evidence from running a check would prevent or reduce further disruption.
Be specific in your reasons. Ambiguous or insufficient reasons will cause delays. Explain the disruption and why you believe the accounts are related, ideally using diff links or other evidence.
Make sure there are no local checkusers or policies.
Reason(s): Sudden supporters for a unknown radical organization. Removing Notability and other tags placed by Admins. Tahir mq (talk) 06:42, 26 February 2014 (UTC)
There is no explanation of why a checkuser should be undertaken, or what would be done with the results. If the users accounts are abusing the wiki, and operating outside of the wikis guidance, then use the tools that you have to manage their edits. If you need assistance of stewards in a broader sense please explain what is required. — billinghurstsDrewth 08:41, 26 February 2014 (UTC)
Reason(s): vote-stacking in the deletion procedure of an article regarding an institution claiming to have $600 billion to buy Greece's National Debt. New users are created in order to vote and disrupt the procedure while some of them constantly conduct revert wars in the article. Geilamir (talk) 18:36, 27 February 2014 (UTC)
Can you please provide more information, including diffs? --Rschen7754 04:24, 3 March 2014 (UTC)
Reason(s): all users are trying to write article Бай Кольо Марсианеца (en:Uncle Kolio The Martian). The article Бай Кольо Марсианеца was deleted after a vote of the members of the Bulgarian Wikipedia --Izvora 17:57, 4 March 2014 (UTC)