You can buy a partly paid share by paying only partially instead of its full issue price. The balance amount for the partly-paid shares can be paid in instalments depending as per the calls made by the company. 

For example, if you are holding 18 shares of a company and the ratio for rights entitlements is 1:10, then you will only receive one rights entitlement for every ten shares you own. If you want to receive two rights entitlements, you will have to buy two more shares.