This pretty much just comes down to knowing the vocabulary. And context – you’re not ever going to be expected to back-convert a verb in a vacuum. And yeah, as you said, the kanji also helps, if you’re seeing it in writing.
Here’s an example: とんだ in dictionary form could be either 飛ぶ (to fly) or 富む (to be rich), but 飛んだ is only ever going to be 飛ぶ. And again, ひこうき が とんだ (the airplane flew) can only be 飛ぶ.
In the case of きった, it’s easy – there are no verbs of the form きつ or きう. =)
If you don’t have kanji or context, the next trick is to start with the most common verb and work your way backwards, but it can get really tricky without kanji or context. For example, かった is more likely to be 買う (to buy) than 刈る (to cut hair), but it could also be 勝つ (to win), or even 飼う (to keep a pet).
And yeah, the すぎる ending attaches onto the ます-stem. 買う -> 買いすぎる