There are two different styles of pyramid-shaped d4 dice:
The purple d4 on the left is read by having the number at the bottom be the result of the roll (in this case, a 1). The light blue d4 on the right is read by having the number at the point be the result of the roll (in this case, a 4).
In both die types, the result is the number that is right side up, and it will be in the same position no matter which side of the die you are looking at. You don't add the numbers from different sides together (they will always be the same), you just look at one side and look at the number that is supposed to indicate the result.
For your specific case of 1d4+4, you would roll a single d4, look for the result on one of the die faces (just one side, don't factor in the other sides; they're the same), and then add 4 to the result. So the left die shown above would be 1+4=5 and the right die shown above would be 4+4=8.
History
The reason for the set mix as it exists is that, originally, the dice available were a set of platonic solids, sold by an educational company and repurposed by TSR. Namely, a tetrahedron (d4), cube (square hexahedron, d6), equilateral octohedron (d8), dodecahedron (d12), icosahedron (d20). This was a "platonic solids" set.
D20's were routinely read as d10's in wargaming, and used for generating percentiles, which made use of the d20 as a d10 or pair as a d100 a standard practice, going back as early as 1972.
A 1938 dodecahedron with 2 rounded faces opposite each other was available in 1938 for stock simulations. ➀ It wasn't used by TSR, but shows the probable origins of the pentagonal dipyramid we now think of as the d10.
Names
As to names - the earliest modern set (with dipyramid d10) I can readily find documented by name is the "Dragon Dice" set from 1981 (as evidenced on the packaging copyright notice), as photographed at Dice Collector. ➁
I can, however, cite TSR "catalogue" from a ©1979 TSR product - Swords & Spells lists the older set as "Multi-Sided Dice Set" in the catalogue extract on the back flyleaf. ➂ It reads:
Multi-Sided Dice Sets — Each set contains one 20-, 12-, 8-, 6-, and 4-sided die
The same title and text was used in the 1975 product list in Strategic Review Vol 1. Issue 3 (1975). ➃
So:
Multi-Sided Dice Set - the original d20 d12 d8 d6 d4 platonic set.
Dragon Dice - the "mud dice" set with d10's.
➀ Dice Collector - Mason & Co Stock Exchange Dice - www.dicecollector.com/MINT39_MASON_&_CO_STOCK_EXCHANGE_DICE.jpg
➁ Dice Collector - TSR - www.dicecollector.com/THE_DICE_THEME_TSR.html
➂ Gygax, [E.] Gary, Swords & Spells, 6th printing, Tactical Studies Rules, 1979. Original copyright 1976.
➃ Tactical Studies Rules, Strategic Review, Vol. 1, No. 3, Autumn 1975, Ed. [E.] Gary Gygax. TSR advert on page 8. From the Dragon Archive CD.
Best Answer
Gamescience, a dice manufacturer, calls such a die simply a d20 0–9 Twice. Yours appears to be this one, and, as of this writing, it appears you can buy more.
However, you may not need to. The owner of such dice usually colors in at least half the numbers himself—wax crayons used to be included with dice sets for exactly this reason, but paint or, I guess, even nail polish works, too—so that to generate a number from 1 to 20, the roller picks either the colored-in or uncolored or differently colored numbers as high. That way an uncolored 0 represents 10 and a colored-in 0 represents 20, for example, and, of course, rolling the same die twice generates a d%.