I see many postings with different opinions about the what evolution is. I decided to contribute my questions and answers:
1. Can evolution be observed? The answer to this question is both yes and no. If you are talking about microevolution, which happens in the genomic level, biologist almost everyday observe or manipulate microevolution, usually by experimenting with the timing and initiation of particular genes. Macroevolution, which happens at the species level, is another story though. It is very difficult (if not straight impossible) to observe macroevolution. In lucky instances sometimes we can get a glimpse of how changes occur (e.g. in a fluctuating environment such as islands, how does birds responds to availability of food; or resource partitioning and eventual sexual isolation of some group of lemurs etc). But that is very rare.
2. Does species transform from one into another? The process of formation of new species is called speciation, and it is important aspect of the macroevolution. As I briefly mentioned in the first question, macroevolution is a really slooooooooow process. We will not be seeing how the modern mammals is going to diversify in our life time. But geologic record provides us, sometimes very detailed (and sometimes very sparse) evidence of speciation (and it is converse extinction). You can look at lineages that has long and very complete fossil records (such as foraminifers, gastropods etc. As complete as mammal and dinosaur fossil records are, they do not come anywhere close to the completeness of marine invertebrates), and see that you can look at a form and trace it is ancestry millions of years back into the time with small but significant difference in the morphology. Granted that where you are going to split these lineages as different species is arbitrary. However, the change of form is real.
3. Do we find ancestors in the fossil record? Again yes and no. This is actually a rather semantical issue and depends on what kind of systematic tradition you have trained. The modern systematics are typically cladist. You can think of clades are infinitely big and elastic storage cabin. You can put more divisions into it, and further categorize things, or you can remove the dividers and lump things into each other. There is only one criteria though. For the clades to be real, all the biological groups included in that clade must share a common anceestor. Now, cladist accept the concept of ancestor. However, from a methodological point of view you can never find an ancestor in cladistic paradigm. Here is how it happens. We have three species, A, B and C. A and B are living today, and C we find in recent fossil record and. When we do a cladistic analysis, the resultant relationship will look like a branching tree, where A and B are more closely related, and C will be outside of this group (or clade rather). However, nothing sits on the trunk of the tree (technically called nodes of tree). All A, B, and C are the branches of the tree, and what the tree is saying that C is more primitive than both A and B, but it does not give you a clue whether it is their direct ancestor.
From a cladistic point of view, ancestors are hypothetical. You can never go out into field, pick up a fossil and argue that this fossil occupies the position of this ancestor. You can say that perhaps this fossil resembles very much the hypothetical ancestor for these groups, but that's as far it will go.
Obviously we all have ancestor. I have my dad, my dad has his dad, and so forth. So, when we find a fossil it is likely to be ancestor to some group (living or dead). But can we methdologically be sure that it is an ancestor. No.