Fertilizer feeds your lawn, just like water keeps it hydrated. You can live for a while on water alone, but you certainly won't be healthy without food. And whilst healthy soil may provide ample food in some cases, most of you may not be so fortunate. This is probably why you are reading this. And, where some of us strive to achieve the perfect lawn, the inconsistencies in the available nutrients in the soil leads us to requiring optimized fertilizing programs for your specific circumstances. It is ideal to conduct a proper soil test, but not an absolute must, especially if you are just getting going. It's a good idea to at least know your approximate soil PH. Please feel free to contact me if you feel you need to get a soil test done. In all circumstances, make it your responsibility to use fertilizers as efficiently as possible! Fertilizers come in all forms. Liquids, soluble powders, granules, pellets, you name it. Is there one perfect solution? No. It is more important to first understand what your lawn needs as a baseline and then you can use the various aspects to tweak performance over time. Even the weather will influence how much of what may need to be applied, so be extra careful. Please feel free to ask should you be uncertain of anything!

Turf grasses require a number of elements to survive and thrive, besides sunlight. Let's go through the basic list:

Essentials: Grass (all plants & living beings) need these to exist

Water (H2O) - all living organisms need water to survive. Contains Hydrogen and Oxygen.
Carbon (C) - is in everything. It is also used by everything living. It also improves the efficacy of everything, and helps make previously inaccessible nutrients, more accessible. Feeds soil microbes, etc. I will shed more light on Carbon as we progress. And yes, your lawn is beneficial to the environment!
Hydrogen (H) - Hydrogen is combined with Carbon during photosynthesis which produces Oxygen.
Oxygen (O) - Is essential for all living organisms.
Carbon Dioxide (CO2) - Your grass takes in CO2 and through photosynthesis, converts it to Oxygen and Carbon.

Macro Nutrients: Grasses need these in 'larger' quantities than the rest of the nutrients.

Nitrogen (N)
Nitrogen, Is at the forefront of turf nutrition and is needed in larger quantities than even Phosphorus and Potassium, which are the other two macro-nutrients. Just like Carbon, Hydrogen, and Oxygen, Nitrogen is essential for all living organisms to produce proteins. Even though Nitrogen is found in the Air, it is mostly not in a form that plants can absorb. However, certain bacteria can convert the Nitrogen from the atmosphere into a usable form for plants. Rainwater also contains ammonium (NH4) and Nitrates (NOx). Even more Nitrates are made available during lightning storms. This is how grass and other plants continue to live, simply by being watered and planted in soil. Nitrogen is loosely termed as being for top growth/leaf growth/greening up, but that is just the tip of the iceberg! Nitrogen does a lot for turf grasses! 
Role: The single most important nutrient for turf! Critical for photosynthesis, encourages shoot and root growth, turf density, colour, disease resistance and stress tolerance.
Excess: Lush soft growth, poor wear tolerance, poor disease resistance, reduced root activity. Increased susceptibility to leaf spot, fusarium patch, take-all patch, brown patch, fusarium blight, grey leaf spot, and makes an easy target for pests.
Deficiency: Pale green or yellowing leaf, reduced growth, Thin sward - low tiller production.
Available at PH: 6-7.5

Phosphorus (P)
Phosphorus is crucial during the initial development stages for turf, such as during seeding or laying new sod. As turf becomes more established, much less Phosphorus is needed. No, not zero Phosphorus. Just considerably less. Too much Phosphorus can eventually produce negative effects on turf, encourage weed and algae growth etc. Phosphorus can often be tied up in soil so unless you are able to make it available, you need to use fertilizers that contain some Phosphorus. You do not need more Phosphorus than Nitrogen 99% of the time. Phosphorus is loosely termed as being for root growth, but it is responsible for many more functions including energy transfer between all parts of the plant.
Role: Seedling development & maturation, Root growth.
Excess: Phosphorous is only required in small quantities for turf grasses & promotes weed and annual meadow grass growth, reduced growth rate of shoots and roots, and in severe cases even death. Excess Phos limits the uptake of many nutrients.
Deficiency: Dark blue-green colouration of leaves, Reduced root and shoot development.
Available at PH: 6.5-7.5

Potassium (K)
Potassium is loosely described as being responsible for all-round plant health. It is also responsible for water regulation and plant metabolism. Potassium helps with disease resistance, wear, heat and cold tolerance. I find that the turf also appears more turgid with the right amount of Potassium.
Role: Increases drought and disease resistance, works as a 'turf hardener', Influences stomata opening and closing, very important for photosynthesis, Disease resistance and it is more available in clay soils. Potassium can leach with relative ease from most soils. Higher potassium levels reduce the occurrence of brown patch, fusarium patch, red thread, dollar spot.
Excess: May cause magnesium deficiency.
Deficiency: Yellowing between veins, Marginal leaf scorch.
Available at PH: above 6

Secondary Macro Nutrients: Grass needs these in relatively 'large' quantities.

Calcium (Ca) - is not only important for plant health but also the soil condition in general. It plays a vital role in strengthening cell walls, and assists cell division and membrane function..
Role: Aids nutrient uptake, helps build a strong plant that's more resistant to traffic and disease pressure.
Excess: Causes Iron, Magnesium and Boron deficiency. 
Deficiency: Reduced root and shoot growth, pale yellow leaves and causes issues when Nitrogen and Iron levels are high.
Availability at PH: 6.5-7.5

Magnesium (Mg)
Role: Critial in Chlorophyll production, activates many enzymes, helps promote winter hardiness and early growth, helps turf use iron and phosphate, and assists in Nitrogen metabolism.
Excess:  Although uncommon, excess Magnesium can limit the uptake of calcium, phosphorus, potassium, iron, and manganese. 
Deficiency: Chorosis, weak turf, poor colour
Availability at PH: 6.5-9

Sulphur (S)
Role: Critical in the utilization of Nitrogen, assists in promoting colour, shoot growth and density, root growth, carbohydrate reserves and reduces disease susceptibility.
Excess: Anaerobic conditions, contributes to black layer when Iron levels are excessive.
Deficiency: Poor growth, colour and disease resistance.
Availability at PH: above 6

Micro-Nutrients: Grass needs these in the smallest quantities.

Iron (Fe) 
Role: Required for photosynthesis, promotes a healthy green colour, assists root growth, improves wear tolerance, and cold and drought tolerances. It is often over-used for a 'green-up' during the colder months.  
Excess: Contributes greatly to black layer, can lead to Potassium and Phosphorus being tied up.
Deficiency: Chlorosis, shriveled looking leaves.
Availability at PH: below 6.3

Manganese (Mn)
Role: Present in chloroplast membranes and functions as enzyme activator. Improves resistance to some diseases. Important for the uptake of Nitrogen.
Excess:  Although uncommon, it can cause oxygen depletion in soil. Toxicity usually only occurs in very low PH soils.
Deficiency: Can cause spotted leaves.
Availability at PH: 5-7.5

Copper (Cu)
Role: Essential for photosynthesis, chlorophyll production. A component of certian enzymes.
Excess: Stunted root growth and leaf chlorosis. 
Deficiency: stunted, withered leaves with a blue-green colour and even dead or brown patches.
Availability at PH: 5-7.2

Zinc (Zn)
Role: Involved in chlorophyll synthesis and amino acid syntheses. Assists certain growth hormone production. Contributes to uniform growth.
Excess: Limits Iron availability.
Deficiency: withered leaves.
Availability at PH: 5-7.2

Molybdenum (Mo)
Role: Component of enzymes that reduces nitrate in plants.
Excess: Although uncommon, it may cause a copper deficiency.
Deficiency: Nitrogen assimilation and potassium absorption issues.
Availability at PH: above 7.7

Boron (B)
Role: Essential in creating new plant cells. Very little required for turf care.
Excess: Yellow or brown leaves, toxic at high levels.
Deficiency: Discoloured leaves, cracked roots, disease susceptibility.
Availability at PH: 5-7.2

Chlorine (Cl) - Plays a role in photosynthesis. Very little required for turf care.

It must be noted that PH, and even soil type can drastically change the availability of certain nutrients.

Is it true that I need to fertilize my lawn once a year?
No, that is the absolute bare minimum. Ideally you need to fertilize for each season specifically. Yes, that means something different for Spring, Summer, Autumn and even Winter!  

How much fertilizer do I need to apply?
The amount of fertilizer required, is directly associated with your soil test results and your desired outcome. Some publications state as much as 4kg of Nitrogen (not fertilizer-just Nitrogen) is required per 100m2 per year. I don't work on that principal at all. I prefer to recommend 1-3KG of Nitrogen per 100m2 per year. How that gets broken up will be determined by season, type of fertilizer, climatic conditions, and current turf condition.