Hobbes believed that humans are exclusively self-interested. In this sense, his views were consistent with psychological egoism (all humans are inherently self-interested).
However, he also believed that in order to gain the greatest benefit to ourselves, we would have to act in the interest of other people. In other words, to maximise our own benefit, we also need to further the interests of others.
So, Hobbes was an enlightened egoist - he realised acting in the interests of others is often the pathway to the greatest benefit to yourself.
According to Hobbes, every human action can be explained in terms of self-interest. For instance, even an adult taking care of a small child could be described as self-interested: the adult knows that the child will have a strong sense of obligation towards them; the adult will have gained a devoted ally.
Hobbes also believed that human beings are rational creatures. Because of our innate sense of reason, we are able to pursue our desires as efficiently and maximally as possible.
Therefore, we are able to formulate the best means to our ends. This may not always result in short-term benefit - instead, the consequences are often long-term. (For example, eating chocolate has a short-term benefit (it tastes good), but not eating chocolate has a long-term benefit (your health is increased). So, as rational beings, we are able to recognize that we should try not to eat too much chocolate!)
The State of Nature
According to Hobbes, the state of nature would be a state with no ruling government or authority. Society would be entirely lawless and, consequently, entirely amoral.
There would be no art, no society, no knowledge.
The state of nature would be unbearable. It would, as Hobbes said, be 'Solitary, poor, nasty, brutish and short.'