Do Latter-day Saints believe they can become “gods”?
Latter-day Saints believe that God wants us to become like Him. But this teaching is often misrepresented by those who caricature the faith. The Latter-day Saint belief is no different than the biblical teaching, which states, “The Spirit itself beareth witness with our spirit, that we are the children of God: and if children, then heirs; heirs of God, and joint-heirs with Christ; if so be that we suffer with him, that we may be also glorified together” (Romans 8:16-17). Through following Christ's teachings, Latter-day Saints believe all people can become "partakers of the divine nature" (2 Peter 1:4).

Do Latter-day Saints believe that they will “get their own planet”?
No. This idea is not taught in Latter-day Saint scripture, nor is it a doctrine of the Church. This misunderstanding stems from speculative comments unreflective of scriptural doctrine. Mormons believe that we are all sons and daughters of God and that all of us have the potential to grow during and after this life to become like our Heavenly Father (see Romans 8:16-17). The Church does not and has never purported to fully understand the specifics of Christ’s statement that “in my Father’s house are many mansions” (John 14:2).

http://www.mormonnewsroom.org/article/mormonism-101#C14