ちひろさん、do you have a dictionary?
If you have an English-Japanese (not online or electric one but the printed one), you'll find a list of 不規則動詞 (verb with irregular conjugation) in it, usually at the end of the book.
If you understand Japanese, this website is useful/helpful.
- 英文法大全 - 英文法 英語 文法 表現 用法 英語学習
英文法大全 All About English
As to the verb conjugation, for example, you can check
動詞 section, and 14-2 動詞の活用 gives detailed explanation on basic conjugation for past and past participle (過去形、過去分詞) with some patterns of irregular ones.
14-2 動詞の活用- 英文法大全 - 英文法 英語 文法 表現 用法 英語学習
As to -ing form, you can find explanation here:
15-3 進行時制- 英文法大全 - 英文法 英語 文法 表現 用法 英語学習
The "-er" you mentioned is to make a noun from a verb to express someone/something that does something (like run -> runner), I could not find a page immediately but the basic is
verb + er (come - comer, speak - speaker, sell - seller)
and double the consonant in the same way as you do for -ing form
(e.g. run - running - runner, swim - swimming - swimmer)
Also note that there are some exceptions which take -or instead of -er.
(e.g. translate - translator, communicate - communicator, direct - director)
The best way is to check with dictionaries.