It helps to understand the difference between a transitive and intransitive verb: this difference exists in both Greek and English.
1 A transitive verb does not make sense without a direct object.
I saw the tiger. The child broke the vase.
He opened the door.
2 An intransitive verb can make sense without a direct object.
She ran to the store.
The children are sleeping.
There are verbs which can be either, and - inevitably - exceptions. For example, 'broke' is transitive above, but 'The vase fell and broke' is intransitive. 'Ran' is intransitive above ('to the store' is not a direct object, and 'she ran' can be used by itself), but 'She ran the charity event' is transitive.
'To sleep' might once have been considered an obligatory intransitive, but now we can say - pax grammarians - 'I slept my laptop.'
All of this is as an introduction to the vagaries of ἀνίστημι.
The basic idea of the verb, as well as its root verb ἵστημι, is 'stand'. It can be used:
1 As a transitive: 'I stand or raise (something, someone) up'. This transitive use of ἀνίστημι is seen with the future active and certain first aorists.
For example, in Acts 2:32, with Ἰησοῦν as the direct object:
τοῦτον τὸν Ἰησοῦν ἀνέστησεν ὁ Θεός
God raised (up) this Jesus
And here is an example in the future:
Προφήτην ὑμῖν ἀναστήσει ὁ Θεὸς
God will raise up a prophet for you (Acts 7:37)
2 More commonly, I believe, ἀνίστημι is used as an intransitive. A person will rise (e.g., from sleep), or stand up (e.g., from sitting). Here are some examples:
ἀναστὰς ἐξῆλθεν καὶ ἀπῆλθεν εἰς ἔρημον τόπον
having risen [Jesus] left and went out to a deserted place (Mark 1:35)
The form of ἀνίστημι used here - ἀναστάς - is an aorist active participle, even though one might think of 'arising' as a middle, i.e., Jesus, the subject, performed an action (rising) which had an effect on his own self.
And, as it happens, here is an example of the future middle being used in a similar way:
καὶ τῇ ἡμέρᾳ τῇ τρίτῃ ἀναστήσεται
and on the third day he will rise (Luke 18:33)
Aargh. For me, it seems less helpful to come up with a detailed set of rules for the use of every form, and - instead - become familiar with the various spellings. Whether the meaning is 'standing oneself up' or 'standing something/someone else up' should be clear from the context.
If we go back to Acts 1:15, where we came across the form ἀναστὰς, we can
(1) parse ἀναστὰς as a masculine singular nominative, aorist active participle, and
(2) recognize that this is an intransitive use of the verb:
ἀναστὰς Πέτρος ἐν μέσῳ τῶν μαθητῶν
Peter, having arisen in the middle of the disciples
Next time - a quicker look at the noun ὄνομα.