~mashou” means “Let’s do something”. For example : Let’s play (Asobimashou). It is as simple as ABC 😉

Examples
Kobayashi : Today, where do you go? – Kyou, doko e (iku)ikimasu ka?
Tony : I will be going to Shinjuku – Shinjuku e ikimasu
Kobayashi : How about you? – Anata wa?
Michael : I will be going to Shinjuku too – Watashi mo Shinjuku e ikimasu
Tony : Then, let’s go together – Jaa, issho ni ikimashou ka?
Michael : Alright, let’s go – Ee, ikimashou
Meaning : Kyou (Today), Doko (Where), Issho ni (Together)

Other Examples
Let’s drink coffee at the coffee shop – Kissaten de ko-hi- o (nomu)nomimashou
Let’s erase off the words on the blackboard – Kokuban no ji o (kesu)keshimashou
Let’s sing Japanese songs – Nihongo no uta o (utau)utaimashou
Meaning : Kissaten (Coffee Shop), Kokuban (Blackboard), Ji (Words), Kesu (Erase), Uta (Songs), Utau (Sing)