First, Group III is the easiest to devide because 来{く}る and する are the only verbs that belong to it. These verbs have each irregular conjugation as you probably know.
Then, if the verb ends with another than ''る'', it belongs to Group I.
For example, you can tell which group 行{い}く belongs to, because it ends with ''く'' which is another than ''る''. Yes, ''行く'' belongs to Group I.
Next, I'll tell about verbs that end with ''る''.
You have to care the previous vowel to ''る''.
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 to Group I.
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 hashiru, 食{た}べる taberu, and 寝{ね}る neru.
Most verbs that end with ''i-る'' or ''e-る'' belong to Group II, so it's easier to memorize verbs that belong to Group I in spite of its feature.
It has been said by rhyaeris, I will mention them again.
The verbs as follows are Group I, however you can't tell which group they belong to only by their dictionary forms.
I dare to give all verbs that I can remember, so there would be some unfamiliar verbs for you.
- 走{はし}る
- 入{はい}る
- 要{い}る いる{LH} (居{い}る belongs to Group II. いる{LH})
- 煎{い}る いる{HL}
- 帰{かえ}る かえる{HLL} (変{か}える belongs to Group II. かえる{LHH})
- しゃべる (It is similar to 食{た}べる, but they belong to another group each other.)
- 滑{すべ}る
- 減{へ}る へる{LH} (経{へ}る belongs to Group II. へる{HL})
- 知{し}る
- 切{き}る きる{HL} (着{き}る belongs to Group II. きる{LH})
- 散{ち}る
- 蹴{け}る
- 練{ね}る ねる{HL} (寝{ね}る belongs to Group II. ねる{LH})
- 限{かぎ}る
- 交{ま}じる/混{ま}じる (It's the intransitive verb of 交ぜる/混ぜる that belongs to Group II.)
- 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 to different group from each other.)
- 焦{あせ}る
- 競{せ}る
- 照{て}る
- 火照{ほて}る
- かじる
- 茂{しげ}る
- いじる
- いびる
- なじる
- うねる
- くねる (It is usually seen in ''曲がりくねる'')
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, 食{た}べます and 食{た}べた are correct not *食{た}べります and *食{た}べった because 食べる isn't in the list above though it ends ''e-る''.