Before getting into the details of what I've been taught on the subject, for those that don't know, we should first establish the three types of love in common Christian teaching. They are based on the Greek words used that are commonly translated as love.
- phileo - properly, to show warm affection in intimate friendship, characterized by tender, heartfelt consideration and kinship.
- eros - romantic love
- agape - properly, love which centers in moral preference. So too in secular ancient Greek, 26 (agápē) focuses on preference; likewise the verb form (25 /agapáō) in antiquity meant "to prefer"
Agape love is considered the purest form of love. To prefer another is to put their needs ahead of your own, and to esteem them higher than others. It is the type of love that we are to have for others, but it's the rarest. It's the type of love that motivates us to willingly lose our lives for those that we love. A parent sacrificing their life so save a child, for example, or Christ's love for us.
The word that's translated as "love" here is the agape love.
Given that, the principle is that we are to put our neighbors first - to prefer them the way we normally prefer ourselves.
You mentioned in the question that there is little self-love these days. That depends entirely on how you define love. Of the three forms, eros and phileos deal with how we feel. Agape deals with how we behave toward another. Agape love is a choice and an action, while the other two are simply feelings, which can change. Generally speaking, agape love is unconditional, and the other two are conditional. We feel them because being with someone makes us feel good. When we no longer feel those feelings, we say we fall out of love.
It's this understanding of love that prompts the phrase "Love is a choice, not a feeling".
When you think about it, for the most of us, barring those that are filled with enough self-loathing to resort to self-mutilation or suicide, most of us put our own needs first most of the time, even if we don't particularly feel good about ourselves.
We eat, rather than starve. We fight to survive in life-threatening situations. We value our own opinions over other people's opinions. We'd rather have our own way, even if we let others have theirs. In general, whether we do so outwardly we think more about our own needs than we do about the needs of others. In short, we are selfish. It's human nature.
And we these things because because we value ourselves. Whether we like to admit it or not, we prefer ourselves over others most of the time. Just like we prefer ourselves over God. "I don't feel like going to Church. I have too much to do to waste time in prayer", etc.
This verse speaks to that and says "Don't be like that. Instead of saying I'd love to help you move, but I have to (Fill in the blank) Instead of thinking of what you want to do, think of your neighbor's needs and prefer (agape love) them. Help them at your own sacrifice."
Perhaps put more simply:
The one who says "I'd love to help you but I need to XXXXXXXX" is preferring himself. Putting his own needs above the one who needs help.
The one who says "Can I help you" when they have something else they'd rather be doing, even (or especially) if what they'd rather be doing is a true need is preferring (agape loving) their neighbor as he would love himself.
It's actually just another form of the golden rule. Do unto others as you would have others do unto you.
A shorter version can be found in Clarke's Commentary on the Bible
The love of our neighbor springs from the love of God as its source; is
found in the love of God as its principle, pattern, and end; and the
love of God is found in the love of our neighbor, as its effect,
representation, and infallible mark. This love of our neighbor is a
love of equity, charity, succor, and benevolence. We owe to our
neighbor what we have a right to expect from him - "Do unto all men as
ye would they should do unto you," is a positive command of our
blessed Savior. By this rule, therefore, we should speak, think, and
write, concerning every soul of man: - put the best construction upon
all the words and actions of our neighbor that they can possibly bear.
By this rule we are taught to bear with, love, and forgive him; to
rejoice in his felicity, mourn in his adversity, desire and delight in
his prosperity, and promote it to the utmost of our power: instruct
his ignorance, help him in his weakness, and risk even our life for
his sake, and for the public good. In a word, we must do every thing
in our power, through all the possible varieties of circumstances, for
our neighbors, which we would wish them to do for us, were our
This is the religion of Jesus! How happy would Society be, were these
two plain, rational precepts properly observed! Love Me, and love thy
Fellows! Be unutterably happy in me, and be in perfect peace,
unanimity, and love, among yourselves. Great fountain and dispenser of
love! fill thy creation with this sacred principle, for his sake who
died for the salvation of mankind!