I recently went to a beach and saw large masses of green and red algae, wondering if I could use this marine algae as a source of nutrition for my plants. If this is effective and not risky, should I distribute the algae on the surface of the soil or bury the algae before planting?
Assuming you are talking about seaweed, it's not exactly a fertilizer as such in that it does not feed plants directly, rather it improves the soil the plants are growing in and is a very good addition to garden soil. Mineral content does vary slightly depending on the particular variety of seaweed, but all varieties generally contain high levels of minerals, in particular, calcium and iodine. It can be added to unplanted beds and borders; some people wash it with fresh water first, but otherwise, it will contain some salt, so adding it to soil directly is usually done some months prior to planting.
Alternatively, it can be added to compost heaps, or composted on its own; once it is composted, it can even be added as a mulch to potted plants. Depending where you live, there may be rules about whether you are allowed to collect and take away seaweed, and only seaweed laying loose on the beach should be collected, it should not be stripped from rocks or wherever it is currently growing.
Further information here https://www.theguardian.com/lifeandstyle/2016/nov/19/why-seaweed-is-great-for-gardens-alys-fowler
There is evidence of seaweed being used as fertilizer for at least 600 years, and probably much earlier than that. In the UK alone, you should be able to find information on the traditional methods used for in the Channel Islands, the west coast of Ireland, and the Hebrides.
One issue is the salt content. This is unlikely to be high enough to cause problems for plants, but it deters worms. Another (more modern) issue is that seaweed tends to accumulate pollution from the water it lives in, so beware of building up toxic residues in the soil.
You can apply seaweed as mulch (though it decomposes quickly) or add it to a compost heap to speed up the composting process.
You can buy seaweed fertilizer commercially, either in powder form to apply to the soil or as a liquid extract that can be used as foliar feed.
Japan, Scotland, UK, CHina there's historic accounts of using Seaweed as fertilizer. Before it was a meal, lobster was used as fertilizer. Ireland as far back as the 13th century. regardless, Yes you can use it. Simply dehydrate it, grind it into a fine powder and apply it to compost. **** However be very careful of the use of it if it's grown in areas with substantial pollution.