Excellent question by /u/curyous in /r/btc . I copy my reply here as I can see this being a frequently asked question, and there is good potential for discussion here :-)

The implementation follows the current UAHF spec which requires the following rather immediate steps regarding blocksize:

• nodes must have a "fork EB" of at least 8MB , i.e. accept blocks up to 8MB .
• mining nodes must configure a mining generation (MG) size > 1MB which takes effect once the fork activates. The default value for this will be 2MB . Miners will be able to raise their block sizes gradually after the fork, as the nodes will support the EB to which they are configured (8MB default, but can configure more).
• Until the fork takes place, nodes are limited to producing up to 1MB blocks like today, and also will not accept or relay > 1MB blocks .
• Mining clients will generate a > 1MB block and all nodes will only accept a > 1MB block directly upon activation (the "fork block"). The following blocks do not have to be > 1MB, only the fork block. This > 1MB block in the chain prevents a re-organization by the legacy chain.

About the longer term:

The UAHF moves the blocksize cap into the domain of emergent consensus (Bitcoin users can now configure it themselves).

Bitmain, in their blog post about the UAHF contingency plan, has laid out their vision of what they think are realistically achievable block sizes over the coming years.

Time - Block size, Byte

• 2017 Aug - 2,000,000
• 2017 Sept - 4,194,304
• 2018 April - 5,931,641
• 2018 Aug - 8,388,608
• 2019 April - 11,863,283
• 2019 Aug - 16,777,216
• After 2019 Aug - Depends on further research

As they self describe, these are figures seen as realistic by miners who are quite conservative and careful by nature.

They have also pointed out proposed mechanisms like BUIP056 to better choose the blocksize dynamically based on what the community of miners are signalling.

No doubt the actual scaling will depend on how much progress is made on things like weak blocks, sharding, and implementation of better parallelism in general in the software.