You are right. Saving can be a solution, but it is only really effective in the short term. When inflation is higher, we have to pay more for the same goods and services. Therefore, the right approach is to avoid unnecessary spending and focus more on increasing our income. That is the real key to dealing with inflation over the long term.
Besides that, we should avoid holding and saving too much in fiat. Instead, we should move part of it into assets that can better preserve value over the long term.
I agree that people should live within their mean and avoid unnecessary expenses. That is the first step to coping with inflation. People mostly get into financial trouble because the way of their lifestyle expenses exceed their income.
I do not think that only reducing expenses is a long term solution, sometime people become fed up with cutting their expenses. They still need housing, healthcare, food and other essentials to survive. If inflation continues while income remains the same then they are left with very less to cut.
I also don't mean that people should start or jump into the businesses about which they know nothing. Increasing income can be done by learning new skills or by taking some part time jobs. They can also invest in different areas if they have significant funds, or they can also start with a small amount. So, that they can improve their economic capacity.