Full answers how did women join the struggle for equal rights? what were their goals?

Women took the activism they learned as civil rights workers and applied, and their goals were to concentrate on the fight for their own equality.

The earliest organised movement for equal rights for women as far as I know was during the French Revolution. The Revolutionary government granted women some important rights, like the right for a married woman to divorce her husband for cruelty or neglect, to retail control of her own property after marriage etc. A group of women activitsts such as pauline leon and the actress Claire Lacombe formed the Society of Revolutionary Republican Women in May 1793, which favoured equal rights for women. it became the object of suspicion of the Committee of Public Safety and General Security, which closed it down in October 1793. 
It wasn't until the mid 19th century that women began to organise themselves in really significant numbers. The Senecca Falls Convention in 1848, organised by Lucretia Mott and Elizabeth cAdy Stanton, laid down specific goals to work for, including better education for women, better employment opportunities for working women, more rights for mArried women etc. Elizabeth cdy Stanton even went so far as to insist on votes for women, which some of the women at the conference thOught was going too far. The Conference was generally ridiculed in the press, but the women persisted and after the Civil War more women joined the struggle for equal rights. 

Race, for example, the chinese exclusion act