First, Group III is the easiest to devide because 来{く}る and する are the only verbs that belong it. These verb have irregular conjugation as you probably know.<br/>


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Then, if the verb ends with another than ''る'', it belongs Group I.<br/>
For example, you can tell which group 行{い}く belongs, because it ends with ''く'' which is another than ''る''. Yes, ''行く'' belongs Group I. <br/>


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Next, I'll tell about verbs that end with ''る''.<br/>
You have to care the previous vowel to ''る''. <br/>
For example, let's watch a verb ''乗{の}る''. This verb can be written ''noru'' in the alphabet, then the previous vowel to ''る'' is ''o''. If the previous  vowel is ''*a*'', ''*u*'', or ''*o*'', the verb belongs Group I.<br/> 


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It's a difficult case for you when the verb ends with ''る'' and the previous vowel to ''る'' is ''*-i*'' or ''*-e*'', e.g. 走{はし}る hash*iru*, 食{た}べる tab*eru*, and 寝{ね}る n*eru*.<br/> 
Most verbs that end with ''i-る'' or ''e-る'' belong to Group II, so it's easier to  memorize verbs that belong Group I in spite of its feature.<br/>
<br/>

It has been said by rhyaeris, I will mention them again.<br/>
The verbs as follows are Group I, however you can't tell which group they belong only by their dictionary forms.<br/>
I dare to give all verbs that I can remember, so there would be some unfamiliar verbs for you.<br/><br/>
 - 走{はし}る<br/>
 - 入{はい}る<br/>
 - 要{い}る    (居{い}る belongs Group II.) <br/>
 - 帰{かえ}る    (変{か}える belongs Group II.)<br/>
 - しゃべる  (It is similar to 食{た}べる, but they belong another group each other.)<br/>
 - 滑{すべ}る<br/>
 - 減{へ}る  (経{へ}る belongs Group II.)<br/>
 - 知{し}る<br/>
 - 切{き}る  (着{き}る belongs Group II.)<br/>
 - 散{ち}る<br/>
 - 蹴{け}る<br/>
 - 練{ね}る  (寝{ね}る belongs Group II.)<br/>
 - 限{かぎ}る<br/>
 - 交{ま}じる/混{ま}じる (It's the intransitive verb of 交ぜる/混ぜる that belongs Group II.) <br/>
 - 過{よ}ぎる  (It has a little similar meaning to 過ぎる and すぎる and よぎる is written in the same kanji, however the two belong different group from each other.)<br/>
 - 焦{あせ}る<br/>
 - 煎{い}る<br/>
 - 競{せ}る<br/>
 - 照{て}る<br/>
 - 火照{ほて}る<br/>
 - かじる<br/>
 - いじる<br/>
 - いびる

 

Memorizing these verbs, you can tell that 走{はし}ります and 走{はし}った are correct, not *走{はし}ます and *走{はし}た, 上{あ}げます and 上{あ}げた are correct   not *上{あ}げります and *上{あ}げった because 上げる isn't in the list above though it ends ''*e-る*''.