You probably want to use a blend state that has alpha blending enabled. When you initialize your program, create a blend state with the following settings:
D3D11_BLEND_DESC blendDesc;
blendDesc.AlphaToCoverageEnable = false;
blendDesc.IndependentBlendEnable = true;
for (UINT i = 0; i < 8; ++i)
{
blendDesc.RenderTarget[i].BlendEnable = true;
blendDesc.RenderTarget[i].BlendOp = D3D11_BLEND_OP_ADD;
blendDesc.RenderTarget[i].BlendOpAlpha = D3D11_BLEND_OP_ADD;
blendDesc.RenderTarget[i].DestBlend = D3D11_BLEND_INV_SRC_ALPHA;
blendDesc.RenderTarget[i].DestBlendAlpha = D3D11_BLEND_ONE;
blendDesc.RenderTarget[i].RenderTargetWriteMask = D3D11_COLOR_WRITE_ENABLE_ALL;
blendDesc.RenderTarget[i].SrcBlend = D3D11_BLEND_SRC_ALPHA;
blendDesc.RenderTarget[i].SrcBlendAlpha = D3D11_BLEND_ONE;
}
blendDesc.RenderTarget[0].BlendEnable = true;
Then before you draw, set that blend state on the context using OMSetBlendState.