How can a lay person approach the learning process of Buddhism?

There are many specific ways, giving you the best way requires a scientific study done on every possible way buddism can be taught and then finding a distinct right answer from that, which is currently, and probably never be available. I will give you a source that teaches you in a very specific and effect way of practicing buddism:

https://www.youtube.com/user/ActualizedOrg/videos

Specifically his meditation videos guide you through to enlightenment very effectively.

Saddha has been referred to as the confidence towards the understanding of Supreme Buddha (Saddhahati Tathagatassa Bodhin). All of us must do everything possible to at least come to Saddha in this life. One cannot go the distance in this Dhamma Path without Saddha.

Therefore we must cultivate right effort (Viriya), the will, to develop Saddha to receive the true benefits from Dhamma. One who has come to Saddha is one of Samma Ditthi (right understanding of the four noble truths). A worthy person. This is not an easy thing. Only a fortunate few would arrive at this.

If we gradually but firmly establish Saddha in us and develop it, our Sakkaya Ditthi (the idea of self) leaves us. The Supreme Buddha preached that this is more delicate a thing than shooting one seventh of a horse hair with another seventh part of a horse hair face to face. A horse hair is taken for this simile because it is thinner than that of a human. To break free, to gain freedom from this notion of ‘self’ or Sakkaya Ditthi is even more difficult, but not impossible.

There are many avenues that can lead us astray. But for Nibbana there is only one road. Only one guide.That single road is thinking that “Supreme Buddha knows. I do not know” (Keetagiri Sutta). The only safeguard for us, in keeping us safe from harm is our association with a Kalyana-Mitta (Noble Friends in Dhamma).

On this ‘Noble Friend’guidance, Ananda, one of many principal disciples of the Supreme Buddha, once asked the Buddha if half of the reason for the spiritual life was friendship with others. The Buddha turned to Ananda, rebuking him mildly with the words, “Don’t say that, Ananda. The whole of the spiritual life is for friendship.” This shows that the Buddha elevated spiritual friendship to the highest status.

If we regard ourselves as knowing the Dhamma well, we will be of the “I am the one who knows” mindset. Without allowing that to happen try to come to the view “I do not know. Only Supreme Buddha knows. I will accept it that way”.

“I am the one who knows” can be equated to a Thorn Bush. It is like this. There is a bush of thorns at the bottom of a hill. When it rains fertile soil settles down round the thorn bush after getting washed down from the hill. The soil is fertile but what gets nurtured is the thorn bush.

Like this it is the fertile soil of Dhamma that we gather round us. But what gets nurtured is the thorn bush called “I am the one who knows”. When the thorn bush grows up even an animal does not approach it. Will not go even passing it. In the same way the biggest danger to a person on arriving at the view “I know”. “I understand” is his becoming a person who does not listen.

He loses his sincere friend. He loses his ability listen to Dhamma well. (He loses both external sources of help). Then what is he left with? Only with the notion “I know” and “I understand”. He keeps on repeating this. Finally he will say “No one taught me. I studied on my own. I do not need anyone now. I will become solitary now”.

This is a big danger. Therefore you always think “Whatever Supreme Buddha taught I will do it in that way”. Think that you are the listener. What we want is to get released from Sansaric Sorrow. That is why Supreme Buddha preached to king Kosala as follows. “Oh Maharaja. This is how you must discipline yourself. I will become a person with sincere friends. I must get inclined to having sincere friends”. (Kalyana Mitta Sutta – Sanyutta Nikaya 01)

When you think that way, the idea “I know” will wear off. Then association with sincere friends becomes delightful.One will always cherish the company of noble friends. One will get the opportunity to listen to Dhamma well. Yonisomanasikara (thinking wisely as mentioned in Dhamma) will arise. This person will develop the Noble Eight Fold path. This happens solely due to association with sincere friends. We must be humble enough to do so.

If one cultivates thoughts of “Supreme Buddha knows…….” I am a person with sincere friends….” no one can prevent us from getting onto the path leading to Nibbana. Chakku Sutta (Okkanthi Sanyutta – Sanyutta Nikaya.03) Such a person is referred to as Sraddhanusari. He will not die until he attains the fruit of Sotapanna (the first stage on the path to deliverance)

Supreme Buddha knows that the person with defilements is wrapped up in the idea of Self, is egoistic. Also that he is wrapped up in the concept “I know”. Some people struggle to understand this simple truth in depth. That is why it is important to think and retain in your memory the following “I will obey Supreme Buddha and conduct myself in the way he wanted us to conduct ourselves. I will not do anything else”.

Getting back to the simile about the thorny bush. When it rains fertile soil comes down to the bush of thorns and it grows up in a couple of days. Ultimately it becomes too big to be pulled out. Sin is also like that. So we must pull out this thorny bush and plant a good tree on that fertile soil. The biggest thorn bush we have is the notion “I know”.

The good tree we plant after uprooting the thorny bush is “Supreme Buddha knows. I don’t know”. These thoughts lift up the man to a noble level. If we are of the idea “We know” it amounts to our tightening our own necks. We read what Supreme Buddha has preached. Then we assume “I know”. Our sincere wish should be that such a thing will not happen to even an enemy.

Therefore if we become humble in this manner we would have done something very much beneficial to our lives. The instant we start having confidence that way, Kammic actions, causing rebirth in the fourfold hells will not take place in us. So to further onself in the Noble Path, the thorn bushes that need to be gotten rid of are “I am the one who knows”. “I can” “I have memorized. Others aren’t up to it”. “I understand well. I can speak well”. You must not have room for these and discipline this mind saying “I will do whatever the Supreme Buddha preaches and whatever my sincere friend tells me to do”.

The immense benefit of understanding the True Path to Liberation has come to us. It is a pity if we let go of it. Therefore let us all try our best not to leave room for those immature thoughts such as “We know”. It is because we do not have confidence that we say “this is impossible” etc. If we step into Saddha we will be able to end our Sansaric journey at most in seven births. Attaining Nibbana is not a dream. Think of establishing Saddha in these principles and think of getting liberated from this sorrowful Samsara.

It is the nature of the person who has developed Sraddha in respect of these principles to endeavour to do it with mind, word and body. Then delight arises in him. Why? Because all his doubts leave him. When there are doubts he thinks “I do not understand. I do not know whether it will be possible” etc.

The hindrances develop in him. Pleasant words, thoughts, deeds do not arise in him. His sense organs are not pleasant. Even the face is unpleasant. If the doubts are to be removed develop Saddha in these principles. Then he will think of the principles. Then he will live in delight. His thoughts, words and deeds will be beautiful. Even the facial expressions will be delightful. There will be no remorse, worries or difficulties in him. He will be inclined to help others. Such a group of people would be like flowers in a flower garden.

He thinks of the good qualities of those who helped him. ‘Ingratitude’ will leave him. The instant he arrives in Saddha, gratitude arises. He meditates without difficulty. He attains concentration. When he thinks of these principles while in concentration he understands “this eye is impermanent….” It becomes a realization to him. Then where did we start? After pulling out the thorn bush called “I know” and instilling Saddha.

It is not correct to have a superficial dichotomy of 'layperson' versus 'monk'. A 'monk' or 'layperson' is a state of mind. For example, some monks spend their life engaged in 'worldly' pursuits; while some laypeople live a personal life of meditative solitude. Therefore, it all depends on your personal goals & intentions in relation to your interest in Buddhism.

If you have suffering you wish to end, you learn the higher ('lokuttara') teachings, like a monk.

If you are a 'householder' (with family, children, etc), you particularly learn the ('lokiya') teachings for 'householders' (as well as the higher teachings about suffering, if you are inclined. Otherwise, you believe in 'rebirth').