The first piece of advice which we can give to those, who start learning the conjugation of Russian verbs, is to learn these verbs in context. Always try to work on phrases but not learn the list of words - it is more effective.
To understand the principles of verbs conjugation, learn how to analyze the composition of a word and to see its stem. Then it will be easy for you to understand what part is not changed and what part we change depending on a pronoun. Also pay attention that some verbs have different stems in infinitive.
Infinitive - бега-ТЬ [bega-T'] - to run
Я бега-Ю [Ya bega-YU] - I run
Ты бега-ЕШЬ [Ty bega-ISH] - You run
Он (она, оно) бега-ЕТ [On/ana/ono bega-IT] - He (she, it) runs
Они бега-ЮТ [Ani bega-YUT] - They run
Вы бега-ЕТЕ [Vy bega-ITI] - You run
Мы бега-ЕМ [My bega-IM] - We run
Infinitive - говори-ТЬ [gavari-T'] - to speak
Я говор-Ю [gavar-YU] - I speak
Ты говор-ИШЬ [gavar-ISH] - You speak
Он (она, оно) говор-ИТ [gavar-IT] - He (she, it) speaks
Они говор-ЯТ [gavar-YAT] - They speak
Вы говор-ИТЕ [gavar-ITE] - You speak
Мы говор-ИМ [gavar-IM] - We speak
It's better to start learning conjugation with two types, so-called "Е-спряжение" (Е - conjugation) and "И-спряжение" (И - conjugation).
The example of "Е-спряжения" - the verb "знать" (to know).
Я знаю русский язык - I know Russian
Ты знаешь русский язык
Он (она, оно) знает русский язык
Они знают русский язык
Вы знаете русский язык
Мы знаем русский язык
The example of "И-спряжения" - the verb "говорить" (to speak).
Я говорю по-русски - I speak Russian
Ты говоришь по-русски
Он (она, оно) говорит по-русски
Они говорят по-русски
Вы говорите по-русски
Мы говорим по-русски
If stress in the verbs of Е-conjugation falls upon ending, the letter Е turns into the letter Ё. These are, for example, such verbs as "жить" (живёшь) - to live, "вставать" (встаёшь) - to get up.
To practise, take a range of verbs, find the stem and try to conjugate them.
Расти - to grow up, работать - to work, стоять - to stand, держать - to hold, корми - to feed