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LingakuLingaku[v5 〜う → 〜い] [v5 〜く → 〜き] [v5 〜ぐ → 〜ぎ] [v5 〜す → 〜し] [v5 〜つ → 〜ち] [v5 〜ぬ → 〜に] [v5 〜ぶ → 〜び] [v5 〜む → 〜み] [v5 〜る → 〜り] [v1 〜る → 〜] [する → し] [来る → 来]
The れんようけい連用形, or ます-stem, is the verb with ます taken off: よみます読みます → よみ読み, たべます食べます → たべ食べ. A う-verb moves its last sound to the い-row, a る-verb drops る, する becomes し and くる来る becomes き来 (き). It is the base that many endings attach to.
Endings like ます, たい, すぎる, ながら, ほう方 and やすい all take this stem. Putting the dictionary form in front of them is the usual mistake.
In writing and formal speech, the stem followed by a comma joins two actions, "and then". In conversation the て-form does this job.
The tense comes from the last verb, as with the て-form. いる and ある become おり and あり here.
Some stems are nouns in their own right: やすみ休み "a holiday", およぎ泳ぎ "swimming", かえり帰り "the way home". Which ones work is a matter of vocabulary, not a rule: you can't make a noun from every verb this way.