How to calcuate the inner product

How would I calculate the inner product of $$|+\rangle|+\rangle$$ and $$\alpha|00\rangle+\beta|11\rangle$$?

I am very new to quantum computing, but I believe for the second problem it would be the probability added? And the probability of α|00⟩ is 1/2 while the probability of β|11⟩ is 0? Let me know if I am way off on this. Thinking along the same lines, I need to find the probability of $$|+\rangle|+\rangle$$ I believe, but I just cannot find how to do this correctly. Again, I am just learning this subject so sorry if this sounds like rubbish. Thanks.

First note that: $$|+\rangle = \dfrac{|0\rangle + |1\rangle}{\sqrt{2}}$$
Second note that: $$|u v \rangle = |u\rangle \otimes |v\rangle$$
Third note that: $$\langle u_1 \otimes u_2 | v_1 \otimes v_2 \rangle = \langle u_1|v_1\rangle \cdot \langle u_2|v_2\rangle$$
I think some clarification on what you're trying to do here would be helpful. Are you trying to find out the inner product between $$|+\rangle |+\rangle$$ and $$\alpha|00\rangle + \beta|11\rangle$$? I'm a bit unclear what you mean when you say "I need to find the probability of $$|+⟩|+⟩$$".
For some state $$|\psi\rangle$$ expressed in the computational basis $$\{|0\rangle,|1\rangle\}$$, one is usually interested in determining the probability of a certain outcome. So for example, if we have $$|\psi\rangle = \alpha|0\rangle + \beta|1\rangle,$$ we can ask, "what is the probability $$P_0$$ of the outcome $$|0\rangle$$ and the probability $$P_1$$ of outcome $$|1\rangle$$?" These are calculated as $$\begin{split} P_0 = |\langle 0|\psi\rangle|^2 = |\langle0|\left( \alpha|0\rangle + \beta|1\rangle \right)|^2 = |\alpha \langle0|0\rangle + \beta\langle 0|1\rangle|^2 = |\alpha|^2\\ P_1 = |\langle 1|\psi\rangle|^2 = |\langle1|\left( \alpha|0\rangle + \beta|1\rangle \right)|^2 = |\alpha \langle1|0\rangle + \beta\langle 1|1\rangle|^2 = |\beta|^2 \end{split}$$ With this in mind, recognize that $$|+\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$$, and $$|+\rangle|+\rangle = |+\rangle \otimes |+\rangle = |++\rangle$$. Now if you were trying to determine the inner product between $$|++\rangle$$ and $$\alpha|00\rangle + \beta|11\rangle$$, we would have $$\langle++|(\alpha|00\rangle + \beta|11\rangle) = \alpha\langle++|00\rangle + \beta\langle++|11\rangle.$$ Hope this helps! If you need more clarification, I'd highly recommend an introductory QM textbook like Townsend, or QC and QI by Nielsen and Chuang. Or just add follow-up comments!