While the above solution is perfectly valid, something different first came to my mind. Using this solution avoids the nasty reality of trying to balance three toothpicks against one other.
Simply allow the toothpicks to overlap. Your first triangle is in the center of the three toothpicks, as shown below:
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Making three more triangles with three more toothpicks becomes simple when you start with this. Here's what it looks like:
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\ / \ /
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Presto, bingo, bango, four triangles. Eyeballing it should get you triangles of fairly equal size. If you're not satisfied with that, use a ruler.
Hey, the original question doesn't say anything about using the entire toothpick.
sam512 notes, "Or just make a Star of David shape - two equilateral triangles superimposed - and you have SIX equilateral triangles!"
Touché.
To which Professor Pi retorts, "The star of David solution is wrong. The additional triangles are not the same size as the original. But your solution is neat."
Which is true, if you start with one of the big triangles. The original question demanded one triangle be created first, followed by an additional three of equal size. However, if you start with a different triangle, it still works. Observe:
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Starting with this gives you a starter triangle the same size as the remaining five in the Star of David:
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\ / \ /
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/__\____/__\
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Three additional toothpicks, five additional equilateral triangles the same size as the first.