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Currently (March 23th), in the currency exchange black market, one dollar will give me 1171 BsF. The minimum wage of Venezuela is 24.853 BsF. So, if I change ~20 USD, I'll get the minimum wage. Is this a lot of money in Venezuela? Or the inflation is so high that minimum wage is unrealistic?

Also I see that there are several exchange rates, if I go to regular money exchange, will I get 1171 BsF per dollar? Or which rate will I get?

Understanding Venezuela exchange rates

tl;dr It may be best not to try to!

First, in case of trawling through old posts and such like it is worth bearing in mind that the symbol Bs. can mean different things at different times. At the start of 2008 the VEB (bolívar) was replaced by VEF (the bolívar "fuerte", which may also be shown as Bs.F.) at the rate of 1,000 VEB to 1 VEF.

Second, there are many different exchange rates between bolívares and dollars. Mises Institute published an article Venezuela's Bizarre System of Exchange Rates in July 2016. It includes:

Few people, however, are aware that many of the country’s problems are caused by a complex monetary arrangement that makes use of four different exchange rates simultaneously. The result is that Venezuela can either be extremely cheap, or unbearably expensive, depending on the rate used.

Third, for a question such as What will $20 buy me in Venezuela? a comparison such as a Big Mac Index ($3.38 for Venezuela, $5.04 for America, in July 2016) is not as reliable as in general, for reasons such as the government subsidies mentioned by @David. It could also mean that checking out hotel prices (as mentioned by @JonathanReez) might not be very helpful if, say, planning to stay with friends. (On the other hand, since any other travel expenses during a visit to Venezuela might be rather less than you expect, the effective rate for hotel costs might be all that is significant for you.) Just as comparison with the minimum wage may not be a good guide since government subsidies are more for what locals buy than for what tourists spend money on.

Vehicle fuel is subsidised and its price may be relevant for your travel. In US terms gasoline is about 1¢ per liter. The official price of one litre of petrol was hiked from about 10 centavos to 6 bolivars in February 2016, at the same time as resetting a key ("first tier", for "essential" goods) exchange rate (Dipro/CENCOEX) from 6.3 to 10 bolívares (fuertes) per USD. What is "essential" is covered by The Central Bank of Venezuela dating from when the tier was introduced in January 2010, at 2.60 VEF per USD.

The SIMADI/(Dicom, "non-essential") exchange rate was floated at the same time but had till then been set at 13 VEF per USD. This is for the purchase and sale to/from individuals and business. Presently around VEF 650 per USD according to the site you link to (dolartoday), it is likely the rate anywhere official. It is expected to reach around VEF 1,000 per USD by the end of next year. The absurdity of it may be why even Travelex do not seem to deal in the currency.

Rates for import of other goods and services were in theory SICAD I (12 VEF per USD) and SICAD 2 (50 VEF per USD) but became irrelevant recently because it has been more than a year since dollars were available for purchase at these rates.
As an aside, CNN reported: Venezuela has more oil than any other country on the planet. But it just bought a bunch of American crude. but the same source (from Feb 2016) includes As oil prices have plunged in the past two years, so has Venezuela's economy, which is now in a severe recession. It's arguably the worst economy in the world. Mismanagement is long-standing and has led to high inflation which in turn underlies the introduction of the new currency in 2008, multiple exchange rates and ever increasing numbers of bolivares required to purchase one dollar.

The Mises Institute report concludes:

The use of several exchange rates has made it easy for the Chávez and Maduro governments and their followers to make enormous profits by embezzling the money assigned to the business community and individuals. By doing so, they have completely devalued the bolivar and impoverished what was once one of the richest countries in the world.

Purchasing power differs according to location. This is normal (lunch in London would probably be a lot more than the same lunch in Newcastle upon Tyne, even if a McMeal much the same in both places) but variation may be more pronounced in Venezuela. According to Numbeo (though data samples may be too small to be truly indicative and all their data is less than totally reliable) even a McMeal in Caracas is 50% more expensive than in Maturín and Meal for 2 People, Mid-range Restaurant, Three-course shows as 2.5x as expensive (beer, on the other hand, a little cheaper!).

Then there is the parallel rate. It floats, so the rate is set in part by your purchases and sales. That means it is a matter for negotiation with whomever you can find to trade with. There are people in Caracas airport who will accost travellers with offers, but they will be nowhere near Bs.F 1,000 per dollar at present.

Because a Venezuelan may be able to receive Bs.1,200 for $1 today, purchased for Bs. 900 only three months ago, dollars are hoarded. This makes them more difficult to acquire for those needing to use them to pay for imports, hence inflation and shortages (see for example Reuters -'We want food!' Looting and riots rock Venezuela daily).

It will depend on where, in Venezuela, and what you want to do. Take into consideration that it will be a good amount of money in terms of services but very little money in terms of goods, since most are imported (including food).
The government grants subsidies to many goods (gasoline, milk, etc.) in order to make them available to people, but other than gasoline, you will have a very hard time purchasing them at subsidized prices since you will need a Venezuelan ID to do so.
Venezuela is a beautiful country and you can have a wonderful time there, but I suggest you make some local contacts before engaging on your trip.
Best providence wishes to you.

Checking out the hotel prices is a good way of estimating travel costs. Current rates at Booking.com start at 60$, so you definitely won't get far after exchanging 20$.

Adding the extremely unstable political situation and severe food shortages means you'll have to pay a lot to sustain a comfortable lifestyle.

In Venezuela there is a strong exchange control and you can not buy foreign currency easily. There are three exchange rates: DICOM, DIPRO and El Dolar Parallel
In the web "Monedas de Venezuela" you can calculate the conversion of the Bolivar to Dollar on the 3 rates
http://www.monedasdevenezuela.net/convertidor-conversor-monedas/